How many of the Scots who came to Ulster were from the Gaelic speaking areas, and how many were from the Scots speaking ones? Furthermore, the Scottish people originally lived in Ireland before coming over to Scotland, so they basically came back to their ancestors’s homes.
I’ve never heard/read anywhere that Scots “lived in Ireland before coming to Scotland”; the history simply isn’t that old (Ireland is one part of Europe with the most recent human inhabitation). The Celts were steadily pushed across Europe from east to west, and the island of Britain was settled by Celts before Ireland.