Ulster as a whole is not in the UK, nor is it in Ireland. It's split between the two. It's a misleading word to use in this context.
There's a hell of a lot of people who don't know the basic facts, I even worked with a guy from Middlesborough on a £100k wage (contractor) who thought that ROI was part of the UK. I guess his lack of geographic and political knowledge didn't affect his ability to churn out Java code.
"Ulster is the UK knacka." Dunno, thought that meant you were saying Ulster was in the UK. Lost in translation obviously.