Immigration has nothing to do with it.

Measles is highly infectious, you need a very high percentage of the population immune in order to maintain herd immunity. So long as you have herd immunity the only source of infection is travel--but note that this works both ways. It's much more likely to be Americans catching it while traveling than immigrants bringing it. They at least used to trace the original case in such outbreaks, it was normally someone who had been abroad.

We saw the same thing with Covid--quarantine against Chinese people, while ignoring Americans returning from the very same places even when they said they had symptoms. (And irrelevant besides, the strain from Europe quickly dominated.)