If those trees are wrong then, you would not be looking in Ireland. Is that right?
Bearing in mind that Timothy married as Horn/e according to his marriage record transcription, have you considered he might have been from a local family rather than the son of an Irish immigrant?
There are Timothy Horns in earlier years but there would seem to be a gap which would be around his birth.
Timothy b 1720 with father Timothy
https://www.familysearch.org/ark:/61903/1:1:J3FJ-8YFTimothy born 1696 with father Simon (could he be father of Tim in 1720)
https://www.familysearch.org/ark:/61903/1:1:NRF3-H4PIt might be best to ignore the ‘people in Ancestry’ who you seem to doubt.
Are those people the same ones who you have Gedmatch connections with but not Ancestry DNA connections?