I am a descendant of Totten's in Co. Tyrone.
Hi Dee,
The 'Totten' surname is so rare in County Tyrone that it is relatively straightforward to narrow down your relative's origins to one or two townlands within the County.
Firstly, in the early 1850s there are four 'Totten' marriages taking place (I realise this is after your John Totten has emigrated but v.safe to assume these are relatives still living in Co. Tyrone) within two areas - Killyman and Pomeroy.
KillymanMary Ann TOTTEN married William Dawson in Killyman Church of Ireland on the 3rd October 1851
Jane TOTTEN married Alexander Young in Killyman Church of Ireland on the 11th August 1854.
PomeroyHenry TOTTEN married Nancy Johnston in Pomeroy Presbyterian Church, Pomeroy on the 22nd August 1851
Margaret TOTTEN married Alexander Hall in Pomeroy Presbyterian Church, Pomeroy on the 4th December 1855.
Secondly, Griffiths Valuation of Ireland has just two 'Totten' households living in the entire county of Tyrone.
The family of Joseph Totten, living in the townland of Gortead, Desertcreat and the family of John Totten living in the townland of Bovean, Killyman.
It would be worth trying to find someone who could look up the individual church records for you and see what records exist for the early 1800s, if any at all.