Most island flying is done as turns. From JFK turns are done to BDA, SXM, PAP, SDQ, STI, POP, LRM, PUJ, MBJ, KIN, CUN, GCM, PLS, NAS, AZS and most Florida cities. The Carib turns are senior because they are very productive. Very senior fly there DH back are done to UVF, BGI, AUA, and CTG. CUR is being added this winter, my guess is it will be a fly there DH back.
Overnights are done in SDQ, STI, BGI, UVF, POS, SJU, BQN, PSE, CUN, AUA, CTG, and all the Florida cities with the exception of SRQ. I would not be surprised if SXM goes back to overnights due to some far 117 issues on the route. Occasionally a rare PUJ and MBJ overnight hits the bid packet.
All South American (except CTG) and most Latin America flying is done by FLL pilots. They overnight in BOG, LIM, LIR, and MDE.
JFK A320 flying is the most diverse, in one trip you can hit the Caribbean and the west coast. E90 is obviously more limited. Boston does similar flying to JFK but with less Caribbean routes. SDQ and STI layovers are junior. AUA a bit more senior. Most can hold UVF and BGI because it's not terribly productive.
There is no such thing as international jumpseating with international airlines. We have ZED benefits with all of them, no priority over any other airline.