AUA's Premed program is accredited. A simple demonstration of this is that AUA's Premed credit has already been accepted in transfer to accredited US undergraduate schools. Colleges and Universities in the US will only accept credit in transfer from similarly-accredited colleges and universities.
Transferring between caribbean schools is a whole different ball of wax. Each individual school will decide how they will or will not accept credit from another institution.
I have never seen a State licensing requirement detailing anything other than "accreditation" as the standard for accepting undergraduate credit to fulfill licensing requirements.
AUA is an accredited degree-granting institution. AUA's Premed program is accredited.
As for ANY student/graduate of a non-US/non-Candian school, it would behoove AUA graduates to have their transcripts evaluate by a
NACES approved agency which converts credit and grades to the US system and denotes similar accreditation.