While modern Irish tartans were designed by Scottish mills, that's not to say definitively that historically the Irish didn't wear tartan.
Splitting hairs here, but in reference to the Ulster tartan, since its age is estimated at around the time of the beginning of the Ulster plantation, and evidence states that the trews were actually made in Scotland, It's probably safe to say that a Scot wore these tartan trews. Remember that in general, Ulster-Scots did not intermingle wi' their "wild" Irish neighbours.

T.