Butch,
The Cullybackey Presbyterian records are not on-line. (Only a handful of Presbyterian church records in Ireland are on-line). A visit to PRONI or the Presbyterian Historical Society (both in Belfast) is required to view them. On the positive side, if that was the family church, their records go back to 1726 when it was built. That’s pretty rare for church records in Ireland.
http://www.proni.gov.uk/guide_to_church_records.pdf
Researchers in the PRONI area: http://sgni.net
There was another Presbyterian church in Cullybackey which opened around 1820. Latterly called the United Presbyterian church (and known locally by some as the Scots Kirk), it has no baptism records before the 1860s. Their earlier records have been lost.
I note from the grave information Miriam found that there was reportedly a Thomas Campbell who remained in Ireland and died in Co. Antrim in Jan 1938. I checked the death records on GRONI and there isn’t a match with that. There were only 3 people of that name who died in 1938. 2 were children and the third lived in Co Down, and died in December 1938.
I found a Thomas Campbell whose father was named Neal/Neill and who married Sarah Mawhirter (McWhirter) on 27.9.1878. He was 20 (so born c 1858). They married at Ahoghill 1st Presbyterian. Tradition was to marry in the bride’s church so that isn’t necessarily Thomas’s church. Thomas was living in Lisrodden in 1878. Here’s that family in the 1901 census, by then in Drumrankin (which is just outside Cullybackey):
http://www.census.nationalarchives.ie/pages/1901/Antrim/Ballyconnelly/Drumrantin/924630/
His age at marriage has him born c 1858 and the 1901 census c 1860. Something similar in the 1911 census:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Ballyconnelly/Drumrankin/115779/
Obviously if he was born after your family had gone to the US then it can’t be the same family. However I note you don’t actually have details of when they left. Perhaps it was after 1858?
There is a possible death for Thomas Campbell on 31.12.1937, aged 77, registered in Ballymena. That’s very close to January 1938! You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
Looking at location, father’s name and the date of death I suspect that may be the Thomas who remained in Ireland. He had 6 children who were still alive in 1911, so there may be some descendants around. I can see a marriage for Agnes Campbell to Andrew McMillan on 12.5.1915 at Ahoghill 1st. So that’s a hint that the Campbell family were probably attending that church then.
https://churchrecords.irishgenealogy.ie/churchrecords/