As far as naming patterns are concerned, both Ireland and Scotland share the same tradition which many – though not all – families followed. There was a fairly narrow set of names and they did tend to get repeated endlessly, generation after generation. It doesn’t mean they are all related, perhaps merely they weren’t very imaginative, or that they were just keen to follow tradition. You can decide.
Your ancestors having a surname often found in Scotland, living in Tyrone and being Presbyterian all point to Scottish roots. Presbyterianism was established in Scotland in the 1550s and brought to Ireland in the 1600s by some 200,000 or so Scots settlers. They mainly settled in the counties of Ulster (including Tyrone).
There weren’t many settlers from the Western Isles at that period. They and other Highlanders weren’t encouraged to come as they weren’t seen as so likely to be loyal to the Crown. They would also mainly have been Catholic then, whereas clearly yours were Presbyterian. (Presbyterianism didn’t make it to the Western isles till the 1700s, and even then a few parts remained Catholic). Most of the Scottish settlers were from the lowlands and southern uplands (the border area with England). They tended to set themselves apart from their Catholic neighbours in Ireland and rather looked down on them. They arrived with an equal number of women, tended to marry their own and kept themselves slightly apart from their Irish neighbours. Having said that there were some Episcoplian Scots settlers, and some Catholics, notably around Strabane. The ones round Strabane were often tenants of the Duke of Hamilton (from Hamilton in Lanarkshire), so not all Scots settlers were Presbyterian. But most were.
As far as Tyrone, Co Derry and Co Donegal are concerned, the Scots mostly arrived through the port of Derry/Londonderry as it was easy to get to. They then spread out across the surrounding countryside over a period of time. (If you are interested in the subject in more detail, Philip Robinsons book “The Plantation of Ulster” explains it well).
It was common for Presbyterian Ministers in Ireland to organize group migration to North America. Having not long moved from Scotland they were more of a mindset to move again than the native population. They started migrating in significant numbers in 1718 but the reasons for going remained valid all through the 18th century and beyond. Background here:
https://www.ancestryireland.com/wp-content/uploads/2017/08/The_1718_Migration.pdf
MacLysaght’s “The Surnames of Ireland” says McKee is “One of the many anglicised forms of Mac Aoidh which in the form MacKee is essentially a north east Ulster name: there is usually a variant of the Scottish MacKay. In Donegal it is numerous as Kee without the prefix Mac.” So your family could be McKays in Scotland.
MacLysaght says of McCoy: “One of the several anglicised forms of Mac Aodha (son of Hugh). Woulfe says it is almost peculiar to Co. Limerick but in fact it is mainly found in North Ulster, where it is a galloglass family".
Galloglass were Scottish mercenaries from the Western Isles brought to Ulster in the period 1200-late 1400s by various Irish chieftains. They were always squabbling amongst themselves and many hired Scots warriors to help defend their lands, or steal their neighbours. They were given land in return for their fighting skills. However the galloglass all arrived pre-Reformation and consequently were almost exclusively Catholic, so I tend to hold with your family – being Presbyterian – coming from the parts of Scotland I mentioned previously, and arriving in the 1600s, not earlier.
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 in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).
You ask whether there would be a strong oral tradition in Ireland. The answer is sort of yes and no. There is considerable interest and pride in our history but as far as genealogy is concerned, the average family probably isn’t that interested and would struggle to go back more than 3 generations or so (ie to about 1900). Unless of course there's a genealogist in the family. Taking Presbyterians as an example, because that’s the relevant denomination in your family’s case, most Presbyterians would be able to tell you that they are descended from Scots who came in the 1600s but only rarely would they know much about where they came from or know the names of those early settlers.
Certain surnames are closely associated with certain locations, and so you can sometimes get a little information from that. For example, a lot of Scots were moved from the Borders to Co Fermanagh in the period 1610-1625. The surnames Armstrong, Hogg, Elliot, Henderson and a dozen others are found today in large numbers in Fermanagh, and also all across the Borders. (Armstrong’s the second most common name in the county after Maguire). So if you are an Armstrong in Fermanagh, you will know your ancestors almost certainly came from the Scottish Borders. Up in north east Antrim a lot of the surnames there are identical to those in Islay and the Kintyre peninsula (McKay being one). The Kintyre peninsula is 9 miles from Torr Head in Antrim. It wasn’t the biggest journey. We know the MacDonalds brought thousands of settlers across in the 1500s and 1600s, so in those situations you can say with some degree of certainty where your ancestors originated. But not every family can be so sure.
