Hi avm228,
Considering they drop of the face of the records after 1907 ** marriage, maybe the the TITSONK isn't an error? ( though it looks like the son became known as "Simmons"?"
** Edit but Carole's 1908 birth looks good

MARRIAGE: John Titsink m Susan Sloman, Mat Qtr 1880 Mile End Old Town
BIRTHS Susan TITSINK, b Sep Qtr 1881 Mile End Old Town. mms Sloman ( see below, she died 1881 also)
BIRTH: George John FITSINK (sic), mms SLOMAN, registered Jun Qtr 1883 IslingtonSCHOOL ADMISSION 1890:
Geo Titsink age 7, born 30 Apr 1883
Admitted 16 Jun 1890. Father John Titsink. 62 Lincoln St
CENSUS 1891: At 62 Lincoln St, Mile End Old Town
Susan TITSINK 32, married, b St Georges East, London
Son: George I TITSINK 7, b Holloway
BURIALS
Susan Titsink,d Sep Qtr 1881 Mile End Old Town.
Buried 23 Aug 1881, Of 431 Mile End Road, Stepney, aged 14 days
In same Grave:
John Joseph Titsink age 29, bur 9 Feb 1892
Elsie Sloman age 69, bur 2 Mar 1895
John Joseph Titsink age 80, bur 7 Jan 1896
Susan Samuel age 49, bur 11 Sep 1907
MARRIAGE: 1900, London City
Susan Titsink and Gabriel Samuel
DEATH: Pheobe TITSINK age 45, reg Dec Qtr 1931, Marylebone
DEATH: George TITSINK age 63, reg Mar Qtr 1946, Islington
Some food for thought!
Cheers
AMBLY