Do you have a source for this? I can’t find anything that says people were evacuated OFF the island in chaos. People were evacuated from some parts of the island to other parts of the island by bus. Are you imagining something like the evacuation from Viet Nam? I think if tens of thousands of Puerto Ricans had been evacuated off the island, it would have made the news.
As far as I can tell, residents who left the island BEFORE and AFTER the hurricane did so on commercial airlines. They have procedures for knowing who is on the plane.