"Legal U.S. citizen" would have covered it.
I agree with you and Williams. It would have been better to say if you are "not a legal US citizen. When "immigrant" was used it was meant in that context. The candidate is running on a strong "anti-illegal immigration" platform. I have no problem with what this candidate was trying to do. Democrats do not like Vietnamese people. They came here not only because they hate communism but also because they believe in the American Dream... those two reasons are enough to make you an enemy of the democrat party.