In general the Scots who settled in Ireland weren’t “forced to leave Ayrshire and removed to Northern Ireland.” Scotland at that time was experiencing a massive population increase and there was also a famine. Good farming land was in short supply. The Scots were offered extensive land opportunities on land declared forfeit when the local Irish rulers fled in 1607 (cf The Flight of the Earls). The rents in Ireland were also lower. So most were delighted to go. No-one was made to go forcibly as far as I am aware, and they were free to return to Scotland at any time they wanted. (Some did, especially after the 1641 uprising).
A good book which covers this history is “Eagles Wings. The journey of the Ulster Scots and Scotch-Irish” by Dr David Hume MBE.