Just out of curiosity of those who traveled to the Caribbean it would be interesting to know the airline they used and if they asked for test results and entrance permission forms before getting on the aircraft.
Delta didn't ask in BOS or EWR for us but, as mentioned above JetBlue did ask in BOS
I traveled down in September to SXM on American from BWI (via MIA). They asked for my approval in Baltimore at check in. And they checked everyone's approval paperwork at the gate in Miami. So yes, at least on American, they wouldn't let you on the plane without pre-approval paperwork.