There’s not a lot I can add to what your researcher told you during your visit. Millsopp (and variants) is not a native Irish name; plus native Irish did not start to migrate from Ireland in significant numbers till the 1800s. Those who went in the 1700s were mostly Protestants (mainly Presbyterian, though not exclusively) who were unhappy with life in Ireland. Having only recently arrived in Ireland, they were more willing to move on, and many did. 200,000 at least moved from Ulster to North America in the 1700s. Nearly all the Protestants in Ireland at that time were people who had settled recently from Scotland, England & Wales during the 1600s. The main Plantation of Ireland started in 1610, though there were some who arrived before that, and quite a lot that came throughout the 1600s.
Belfast in 1679 was a very small settlement. Population of no more than 1500. (Until Belfast started to develop as a city, the capital of Ulster had been Carrickfergus, 15 miles away on Belfast Lough.)
I looked in the Muster Rolls for c 1630 and there are no Millsopps listed, suggesting the family may not even have arrived in Ireland then. Or if they had, there certainly weren’t many of them. Likewise there are no Fullers in the Muster Rolls. There were 2 Fullertons in Tyrone but that’s all. So again the Fullers were not heavily represented at that time. Ancestors born c 1627 & 1630 were very likely first generation descendants of parents born outside Ireland.
This site says Fuller is an English name found in Ireland since the 16th century. It has no information on Millsapp, probably because it is so rare (just 2 of them in Ireland in Griffiths Valuation). That scarcity obviously fits with it being an incomer’s surname.
So the location (ie Armagh, Tyrone and Belfast) point to settler origins, the apparent likely denomination (Church of Ireland) also points to that. (Most native Irish were RC). The timing of their departure from Ireland ie late 1600s (when few native Irish were leaving) also points strongly to the family being descendants of settlers, probably from England as the name seems more English than Scottish or Welsh. And as I say, the family could only have been living in Ireland for a very short period of time, if they had left by 1700.
I looked in the 1901 census of Tyrone. There were no Fullers living there at all. 49 Millsapp/Millsopp in Ireland (mostly Church of Ireland, about 10 RC). Counties Derry, Armagh & Antrim.
You will struggle to trace your ancestors in Ireland, because there are next to no records for the 1600s. Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project and can offer FTDNA testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).