Some other sources say her mother was Hannah Danby, niece of Sarah Danby. This seems to me very unlikely.

From Lisa DeGarston
Evelina was baptized Evelina Turner on 19 September 1801 in Guestling, E Sussex daughter of William and Sarah Turner.

Parish Records Saint James, Westminster. Middlesex
Joseph Dupuis and Evelina Turner both of this parish were married by Banns this thirty first Day of October in the Year One Thousand Eight Hundred and Seventeen by me Edward Tindley? Clerk in Orders.
Signed Joseph Dupuis and Evelina Turner
In the Presence of Charles Thomson and Sarah Danby
[Note Evelina used the last name Turner not Danby. Also since Sarah Danby witnessed this marriage as she did with her daughter Teresa, this might give credence to the interpretation that Evelina is Sarah Danby’s daughter and not Hannah’s. As well, might Charles Thomson be related to Evelina’s sister Georgiana’s husband, Thomas Thompson?]

In the 1861 census 44 Queen Square.
Joseph Dupuis, head, married, age 67, Retired Consul, born St. James, London.
Wife Evelina Dupuis, age 58, Annuitant, born ???? Hastings.
Daughter Rosalia A. Dupuis, age 33, governess, born St Pancras, London.

In the 1871 census 152 ??? Rea? Lane, Lambeth, London, subdistrict Lambeth Church Second.
Joseph Dupuis, head married, age 82, Retired Consulate Supero?, born London.
Evelina Dupuis, wife, age 67, annuitant, born Guestling, Hastings.
Daughter Rosalia A. Dupuis, unmarried, age 46, born Hampstead Road.

In the July to September 1874 death index, Evelina Dupuis, Lambeth district, London, Surrey, volume 1d, page 257.

National Probate Calendar
19 November 1874 Administration of the effects of Evelina Dupuis late of 135 Upper-Kennington-lane in the County of Surrey Widow who died 29 August 1874 Upper-Kennington-lane was granted at the Principal registry to Rosa Dupuis of 291 Commercial-road Peckham in the said County Spinster the Daughter and one of the Next of Kin. Effects under 50 pounds, Resworn January 1875 under 800 pounds.

Findagrave.com
Evelina Turner Dupuis
Birth 1801, Hastings, Hastings Borough, East Sussex, England
Death 29 Aug 1874 (aged 72–73), Lambeth, London Borough of Lambeth, Greater London, England
Burial Kensal Green Cemetery
Royal Borough of Kensington and Chelsea, Greater London, England
Memorial ID 234193710 ·
"Evelina, daughter of William and Sarah Turner" was baptised at Guestling in Sussex on 19 September 1801. She was the illegitimate daughter of the artist Joseph Mallord William Turner and Mrs. Sarah Danby, widow of the composer John Danby. Evelina Turner was married on 31 October 1817, at St. James, Piccadilly, to Joseph Dupuis.

From https://blogs.bl.uk/untoldlives/2021/07/jmw-turner...-part-1-evelina.html
06 July 2021
JMW Turner’s Daughters – Part 1 Evelina
Shortly after the musician and glee composer John Danby died, aged 41, on 16 May 1798, his widow Sarah began a relationship with the artist JMW Turner, who was a near neighbour in Covent Garden.  Their daughter, Evelina, probably named after the title character of Fanny Burney’s novel, was baptised at Guestling in Sussex on 19 September 1801.  The register records her as ‘Evelina, daughter of William and Sarah Turner’.  According to the 1861 census, she was born in Hastings.  In 1811, a second daughter, Georgiana, was born.
In the early years of their relationship, Turner lived with Sarah for short periods of time at various addresses, but this was never a permanent arrangement and they never married.  Turner did not spend a great deal of time with his daughters, although some of his friends reported seeing young girls with a family resemblance, from time to time, at his Queen Anne Street house and gallery.  They are also thought to appear in some of his paintings, notably Evelina in 'Frosty Morning' (1813) and both in 'Crossing the Brook' (1815).
On 31 October 1817, sixteen-year-old Evelina married 28-year-old Joseph Dupuis, a civil servant, at St James’s, Piccadilly, under the name of Evelina Turner.  Her mother, Sarah Danby, was a witness but Turner did not attend.  Joseph Dupuis had a long career in the diplomatic service.  In 1818 he was appointed British Envoy and Consul to Kumasi, part of the kingdom of the Ashanti (now Ghana).  He became regarded as an expert on African affairs, although some of his superiors felt that he had made too many concessions to the Ashanti.  Between 1819 and 1832, Evelina gave birth to seven children, four of whom survived infancy.  In the 1840s the Dupuis family moved to Greece and then back to London in the 1850s.  According to the census records, they were living at 44 Queen Square, Bloomsbury, in 1861 and at 135 Upper Kennington Lane, Lambeth, in 1871.  Their unmarried daughter, Rosalie, lived with them at both addresses.
Dupuis had incurred heavy debts and, following the death of Turner’s housekeeper Hannah Danby in 1853, he applied, unsuccessfully, to manage Turner’s gallery in Queen Anne Street.  Evelina had been left £50 in Hannah Danby’s will, with the stipulation that it was not to be used to pay her husband’s debts.  She was amongst those who challenged Turner’s will and when it was finally proved in 1856, she received, in addition to £100 a year from the original will, annuities based on £3,333 worth of Turner’s 3% consols.  This was clearly not enough because, in November 1865, Evelina wrote to Jabez Tepper, the solicitor who had represented various Turner cousins, asking for help to ‘alleviate the sorrows which oppress the last lineal descendant of the race of Turner, the surviving daughter of an artist of such repute’.
Dupuis’ debts must have been substantial because when Evelina died of a heart attack in Lambeth in 1874, a few months after her husband, she left an estate of less than £800 to her daughter Rosalie.
David Meaden
Independent Researcher
Further reading:
Selby Whittingham, ‘JMW Turner, marriage and morals’, The British Art Journal, Vol. 15, No. 3 (Spring 2015), pp. 119-125
Franny Moyle, The Extraordinary Life and Momentous Times of J.M.W.Turner (London, 2016)
Anthony Bailey, Standing In The Sun – a life of J.M.W.Turner (1997)

In the Christening records Westminster London.
December 27, 1789, Joseph Dupuis, born November 1789, Father Lewis Dupuis, mother Sarah.

From the Danbys by Selby Whittingham.
HM Consul 1811 to 1842
Greece 1851?
Covent Garden 1853 to 1856
Bloomsbury 1857 to 1865
Lambeth 1871 to 1874

From the January to March 1874 death index Joseph Dupuis, age 84, Lambeth district, Greater London, Surrey, volume 1d, page 276

From Lisa DeGarston’s ancestry web site
Joseph Dupuis was appointed British Envoy and Consul to the town of Kumasi, (Ghana) heart of the kingdom of the Kings of Ashanti on 26 January 1818.  He and his wife, sailed on the Sarah to Cape Coast (coastal capital under British control) and arrived on 24 January 1819. His main objective was to instigate of peace between the Kings of Ashanti and Dwabin and to initiate peaceful trade between the Ashanti and the British. A Select Committee of the House of Commons had recommended that the African Company should continue to administer it West African settlements, but should be responsible to a Governor appointed by the Crown.  Although no action had yet been taken on its recommendations, the Colonial Office was beginning to take a more active interest in West African affairs.
Dupuis did not make himself popular with the local Europeans but seemed to get on well with the Ashanti King.  Joseph Dupuis wrote a book on the Ashanti Kingdom, its history, customs and his travels within the territory and his efforts to negotiate a treaty.  The book Journal of a Residence in Ashantee was first published in 1824, presumably to explain the history behind the war in 1824.  It was reprinted in 1966 and in Introduction to the 2nd Edition, W E F Ward comments; Dupuis' stay on the Gold Coast is a sad story of a man with sound ideas who was his own worst enemy and raised up so much opposition to himself as a man that his sound ideas of policy had no chance of being accepted.  In his negotiations at Kumasi, he made only one serious blunder, when he explicitly conceded the Ashanti claim to sovereignty over Cape Coast instead of reserving the British position on the point.  If Hope Smith had been anything of a statesman, he would have realised that Dupuis had made a good impression at Kumasi, and raised the Ashanti's hopes of lasting settlement; and he would have tried to follow up Dupuis' work (remedying its weaknesses if necessary) so as to bring about a settlement which was as much in the Company's interests as in those of Ashanti.  He would never allowed the Ashanti ambassadors to take back the presents to Kumasi and leave Ashanti waiting in vain for news of Dupuis and his treaty.  That is the truly lamentable fact about Dupuis' mission; that Hope Smith and his colleagues snubbed the Ashanti because they disliked Dupuis and thus helped bring about the McCarthy war.

From Wikipedia
https://en.wikipedia.org/wiki/Joseph_Dupuis

Findagrave.com
Joseph Dupuis
Birth Nov 1789, London, City of London, Greater London, England
Death 1874 (aged 84–85), Lambeth, London Borough of Lambeth, Greater London, England
Burial Kensal Green Cemetery
Royal Borough of Kensington and Chelsea, Greater London, England
Memorial ID 234193786
British diplomat appointed as Consul and Vice-Consul for the British Government between 1811 and 1842, with a number of postings to Africa during that period, including one as Vice-Consul in Mogador.

He was baptized 27 Dec 1789 at St. James', Westminster, the son of Louis Dupuis and his wife, Sarah (Cass) Dupuis.