Hi Alison,
The source is taken from the birth of their first born child and son John Cadwalader bapt. 1 Aug 1779 in Guilsfield.
It reads: "1779, 1 Aug, John son of John Cadwalader of Tirymynych and Mary his wife was baptised".
By the time of their second child David, they had moved to Garth and latter records show they had then moved to Llan.
From what I can see this is the only record that mentions him being from their, which means that the researcher made an assumption that based on the 7 month difference between his marriage and first child he lived at Tirymynych. This of course could be the case, however it could mean he was from somewhere else when he married but had moved to there by the time of his first child.