I'd say for mostly anyone, you're a true XYZ if your family's been there for 3 generations or more. That isn't to say 1st/2nd generations are fakes/frauds/outsiders/not welcome, just they're perhaps not fully integrated, which isn't necessarily a bad thing. Rather by the 3rd generation you can usually solidly say they're just XYZ as opposed to ABC-XYZ (i.e. Swedish-American). But it also depends on how much of the host(?)'s country's culture they've adapted and how well they otherwise "fit in" in rough terms.
....Yeah, there's no real good sounding way to put that, is there? By my own mathematical conclusions, my parents aren't exactly American either, since both of their parents came from other countries, meaning I'd be the first (note the "") """"""""real"""""""" American in the family.
Edit:
Major-Tom wrote:If that's how they choose to identify, sure.
This too.