I find a lot of Europeans - particularly Irish - to get unduly upset when Americans use the term "Irish" to mean "Irish American". Sometimes it gets downright childish, ie "you're not really Irish we are!".
9/10 they aren't using it to mean 'Irish American' though. Many, many Americans I know and have met claim to be 'Irish' despite they and their parents never having set foot in the place and they genuinely mean they are of Irish nationality. Sure it can be used as shorthand for 'Irish American' but that's generally not what is meant (in my experience). Ireland's diaspora is more than 10x the country's population so it's definitely not something we rebel against or dislike. There are LOTS of people abroad who can rightly claim to be Irish. When you claim it with virtually no actual ties to the country mainly so you can try to claim some stereotype it's irritating. Irish people are generally pretty proud of our American links and contributions. "you're not really Irish we are!" is not a thing.
Of course they mean Irish American. What else could they mean? I don't think the Irish (in Ireland) are even on the radar. There's a real misunderstanding Europeans have of the European diaspora in general - they think they can understand it in the context of still being in Europe, but you can't.
People should pick up on the context a bit.