Are we talking Caribbean or like "I'm from Indian, and came to the US because it's nicer." Either way, as long you aren't doing because you want to go to the Caribbean who cares? We have a world renowned cardiologist/electrophysiologist here in town and wouldn't you know it he went somewhere in the Dominican Republic.
Doesn't matter because in your amcas you just list the docs name and speciality, not where they got the degree. Besides med schools don't care about that, and there are many good FMGs that you can shadow.