I think the references you have found to Thomas & Andrew were in the tithe applotment records for Newtownhamilton parish in 1830:
To be in the tithes you had to land (it was a tax on land) so in 1830 they both had farms.
Neither is in Griffiths Valuation which, for Altnamackan, were compiled in 1864. There were no Rowan farms there then, so that indicates Andrew had either died or moved away. And Thomas had left some 33 years earlier.
I had a look in the PRONI e-catalogue to see if there are any documents relating to your family in Altnamackan but none is listed.
If the family attended Clarkesbridge Presbyterian church then firstly that hints strongly that they originated in Scotland (but probably in the 1600s). There are no Rowans listed in Armagh in the Muster Rolls c 1630 implying they arrived after that. There was widespread Scottish migration to Ulster in the 1600s. Some 200,000 Scots settled there (representing something like 20% of the entire Scottish population). Some came in the Plantation 1610-1625, others followed throughout the 1600s with a big surge in the 1690s due to famine in Scotland. A few may have arrived in the 1700s but by then the Scots were starting to leave again for North America and elsewhere, so anyone arriving then was bucking the trend. In my opinion, Thomas’s parents were likely born in Ireland.
Secondly, Clarkesbridge only has baptism records from 1822 and marriages from 1840. Possible earlier records were either never kept or have been lost. So you won’t find baptisms for Thomas or Andrew, nor is it likely you’ll find any marriages for either of them. Presbyterians generally don’t keep any burial records. You might find a gravestone for Andrew (assuming he died locally) but that’s probably it.
You say Thomas’s wife Agnes was born in Ayr c 1796. I have checked Scotlandspeople too and can’t find a marriage. However like Ireland, not all parish records have survived and so the church records are far from complete. Or the couple may have married in Ireland.
You are up against what researchers in Ireland call the 1800 barrier. It is very difficult to get back any earlier than that due to a general lack of records.