Sure, I agree you should call them that. "Expat" is short for "expatriate" which is about where they come from. They are both expatriates of America and immigrants to wherever they go.
I'm just pointing out that the most plausible reason your fellow countrymen choose to call themselves "expats" wherever they go, is because the rhetoric in your country has dehumanized or made the word immigrants/illegal "dirty".
Not hard to imagine such rhetoric can lead to nastiness all around, ending even in violence against said group. If you don't mind that and see no problem with that, then of course there's absolutely no common ground for us to have any discussion on :)
Heh I guess you've never been subject to taunts such as "go back to your country illegal" or "you don't belong here!". Must be nice!