The area of Scotland called Argyll was, called Dál Riada in the era that we are considering. Archeologists have always said, and continue to do so, that there is no evidence of a movement of people from Ireland to Scotland in the centuries before St. Patrick. There is however, a lot of evidence of movements from the south of Ireland (and back) to Wales and Cornwall in this era, so the lack of evidence for Dál Riada is telling. Dál Riada at that time spanned both sides of the sea between Scotland and Ireland, but were based in Ireland north of Belfast. It was considered an Irish kingdom and were part of the Uladh alliance.
Accepted history tells us that during the entire 6th century, the Northern O'Neill, based in what we now call Donegal, were pushing east into the area which would later be called Tyrone and Derry. The rulers of that area were the Dál nAraide (sometimes called Cruithin) who were part of the Uladh alliance, but not the dominant part.
In the late 6th century, the Dál nAraide were pushed back into the area later known as Antrim and were based near the modern Antrim Town near Belfast. Under their pressure, the ruling family of the Dál Riada moved to Scotland and were based there in the future so that they became a Scottish kingdom and no longer controlled any part of Ireland. At the Convention of Druim Cett in 575, the question of the Dál Riada fleet was settled. The Dairfhine could rule from Scotland, but their fleet was to be at the service of the King of Tara, i.e. an O'Neill.
The Convention of Druim Cett in 575 was sponsored by the O'Neill and the church and St. Colm Cille was a leader at the Convention. He was also a member of the Cenél Chonaill Dairfhine and they were a prominent part of the Northern O'Neill. He founded the great monastery of Iona off the coast of Scotland.
The one missing group from the Convention was the most prominent part of the Uladh alliance, the Dál Fiatach who were excluded by the O'Neill and as a result of this, the Dál Riada (in Scotland) became an O'Neill ally for some centuries instead of being subordinate to the Dál Fiatach in Ireland.
Note: the Dairfhine was the 'Ruling family' sometimes called a second-cousinage used by kings in ancient Ireland. (A smaller group called a Fine which comprised just first cousins, was used by most others.) They chose the king and the next king came from them. Members were sometimes murdered or blinded by the king, but they were also his important allies against the world. The members were determined as follows. Take a king of a Tuath (petty kingdom) and look at his great-grandfather. Any male descended from that grandfather down to the king's second cousins (but not beyond) was in the Dairfhine. When a king died, his grandfather was the determiner of the next Dairfhine which meant the dead king's second cousins (and their descendants) had lost a lot of power.