IB operates/offers connecting flights to many latin american and island destinations from MIA. IB connects passengers who have flown the Transatlantic sectors from Spain to MIA, onward on smaller aircraft since the demand is not always great enough for the widebody service. It's kind of like a many hub for them.
IB has 4 A319 based at Miami and they fly connecting pax from Spain to Central America. (Guatemala/ Panama/ Costa Rica/ and so on). There 2 daily flights from Mad to Mia operated by 747 and A340. Then passengers flying to those other destinations transfer at Miami Airport.
I think they overnight those A319 in Panama City and San Jose (longest routes). Other destinations are connected with the night flight MIA-MAD.
But I'm not sure, one of our Spanish friends must tell us !!