The History of the Tyldesleys of Lancashire published by John Lunn in 1966 provided little coverage of the family outside the county—such as the branches which settled in Fornham St Genevieve and the Isle of Man.
A good introduction to the latter branch is be found on the excellent Manx Note Book site and is copied below by kind permission of Frances Coakley. This is a transcript of manuscript notes made by A W Moore in 1889 with footnotes by Joyce Oates and Frances Coakley:
From Manx Families, A.W.Moore, MS 1889Tyldesleys of 'The Friary'
Arms: 'Three Rush Hills Vert.'The Tildesley's of Tildesley in Lancashire were an ancient family. The first of them to have any connection with the Isle of Mann was Thurstan de Tyldesley, who was one of two commissioners sent there by Sir John Stanley in 1417. He married Margaret, daughter and coheir of Jordan de Worsley. From his time to that of Thomas, the fifth in descent from him, none of the family seem to have lived in the Island. Thomas was Water Bailiff in 1532, and in 1540 Deputy Governor. He died in 1554. He married a daughter of Sir Alex Radclyffe of Ordshall, Kent, and had issue. His eldest son Thurstan succeeded to the Lancashire property, but it would appear that there was a younger son who had the Manx property, the Friary, called Bemeccan, in Arbory, which had been presented to Thomas in 1536, as there is a William Tyldesley, probably Thomas's grandson, entered for it in 1595. William was a Member of the House of Keys from 1609 to 1637. He died in 1643, and was succeeded by his son Richard, who was made Comptroller in that year. He was the last member of this family, except Stanley, who held a post in the Council. He married Isabella Norris and had issue Thurstan. Richard's son Thurstan, an M.H.K, followed him in 1679, Thurstan's son William  in 1704, and William's son Richard  in 1726. Richard married Ann Stanley,  eldest daughter of Edward Stanley of Preston, a branch of the Derby family, and had issue Richard, who was entered in 1750. Richard married Catherine Moore  and had issue Thomas  (born 1733); Stanley (born 1735) ; Elizabeth (born 1730); Ann (born 1737); Richard (born 1740,  died 1774 without progeny); Edwin and Esther  twins (born 1743). Thomas married Catherine Quayle and had issue (1) Margaret, born 1774; (2) Thomas,  born 1776, died 1798 without progeny; (3) Richard, an officer in the 39th Regiment (died unmarried at Guadaloupe in 1805) . We find it recorded that Richard and his wife settled 'for certain considerations upon their son and heir Thomas and Catherine his wife, the Friary, Ballabilbert, Balladuke, and Billown. Richard was the last of the family who was a Member of the House of Keys, all his predecessors having been either members of that body or of the Council. His second son, Stanley, married Jane daughter of John Allen, heiress of the Hague Estate. There are no representatives of this branch. As none of the sons of Thomas had issue, the estates went to his daughter Margaret,  who married Benjamin Greetham  in 1795, whose issue's descendants are still in possession. Richard, who as mentioned died at Guadaloupe in 1805, was the last of the name of Tyldesley in the Isle of Man.
1 JMO: William Tyldesley md 11 July 1701, Malew to Mary Harrison (father Richard Harrison, mother Ellinor Fargher als Harrison als Norris, who died 7 Jan 1724/5, buried at Peel Church [Malew bur reg: Mrs. Ellen Fargher als Norris, of Skilbreck, buried at Peel Church, 7 Jan 1724/5; also German bur reg: Mrs Ellinr Ffargher als Norris bur in the Church of Peel 9 Jan 1724; see Archdeacon Will 1724/5 #110, Malew of Ellinor Fargher als Harrison als Norris of Skilbreck, made 22 Nov 1722])
2 JMO : God’s Acre, by Feltham: MI, Arbory: "Mrs. Anne Tyldesley alias Stanley, wife of the said Capt. T., died 25th April 1772, age 68. Captn. Tyldesley, of the Friary, died July 11th, 1781, age 80." If Richard (~1701-1781, & who married Ann Stanley) is the son of Richard (d 1750), then Richard (d 1750) must be the brother of William (d 1726 (? 1722) & married Mary Harrison 1701), with Wm (d 1726) dying without progeny
3 A branch of these Stanleys owned Ballacaighan
4 JMO: Richard Tyldesley md 6 June 1747 Braddan to Jane Moore. Is this the Richard who died 1750, without children, and who was the son of William, and was the cousin of Richard 1701-1780? And did he marry Jane Moore, not Catharine Moore? [FPC see Will of Thomas Moore,1762 which gives Nicholas T as husband of Catherine]
5 JMO: Thomas (born 1733); Stanley (born 1735); Elizabeth (born 1730); Ann (born 1737); Richard (born 1740, died 1774 without progeny); Edwin and Esther twins (born 1743): These are the children of Richard Tyldesley and Ann Stanley
6 JMO : Arbory bur reg: Stanley Tyldesley bur 7 Mar 1819.
7 JMO: Richard b 1740 (father Richd, mother Ann Stanley): Arbory bur reg: Richard Tyldesley son of Capt Richd Tyldesley & wife Mrs. Anne Stanley, bur 11 Aug 1744
8 JMO: Arbory bur reg: Esther Tyldesley dau of Capt Richard Tyldesley & wife of Mrs Anne Stanley, bur 8 Sep 1744
9 JMO: Capt. Thomas Tyldesley md 20 Aug 1771 Malew to Catherine Quayle. MI, Arbory, stone I2: Captain Thomas Tyldesley died May 5th 1783, aged 50 years. Cath. Tyldesley als Quayle,died Sept 27th 1780, aged 39 years. Wm, their son, aged 5 months. Sacred to the memory of Richard Tyldesley Esq., of the Friary in the Isle and a Lieutenant in the 30th Regiment who died in England on the 21st July 1791 in his 21st year. Thomas Tyldesley junior of the Friary, died April 11th 1798, aged 22 years. –Arbory Index & All Yards, published by IOMFHS 
10 JMO: Richard was born 20 Dec 1772, Arbory. God’s Acre, Feltham: MI, Castletown Chapel: "On a neat marble. Richard Tyldesley, Esq., of the Friary, Lt. 39 Regt. foot, who died at Guardalope, 21st July, 1794, aged 21. He lived highly esteemed and died much regretted."
11 Margaret md 14 Nov 1795 Arbory, to Benjamin Greetham
12 FPC: Bejamin Greetham was a merchant from a family of merchants in Liverpool, Margaret was apparently his 2nd wife, his father was Isaac. Gore's 1790 directory lists under name Greetham:James, gent, 21 St James St
Isaac, merchant, Harrington. Herringhouse, 12 Grayston-street; Cooperage 23 Grayston st
Benjamin & co ship chandler and paper warehouse, 17 South Dock
J. victualler, Christian street, Islington
Bejamin, Ship Chandler, Harrington, Park Road ; rope walk 5 St James street
Charles Merchant, St James', Harrington Park Road; Porter and Earthernware warehouse, 5 Salthouse lane, South dock
James, gent 23 St James st
Isaac, merchant Harrington; compting house 12 Grayson Street Shaw's alley
Thomas, Ship Chandler St James Harrington, Park road