CTLR AT PBI ARPT DID NOT INSURE A LNDG ACFT WAS CLR OF RWY BEFORE CLRING A DEP FOR TKOF.

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IT WAS APPROX XX30 WHEN WE WERE ARRIVING TO LAND IN PBI. THE APCH CTL SEEMED KIND OF BUSY FOR THE TIME. WE WERE SEQUENCED WITH APCH AND TOLD TO CONTACT PBI TWR. WE CALLED THE TWR 3 TIMES BEFORE THEY FINALLY RETURNED OUR CALLS. WE WERE CLRED TO LAND ON RWY 27R BEHIND OTHER LNDG ACFT. WE WERE ALSO TOLD TO PLAN MINIMUM TIME ON THE RWY FOR LNDG AND DEPARTING ACFT BEHIND US. UPON XING THE THRESHOLD OF RWY 27R; WE HEARD THE TWR CLR AN ACFT TO TAXI INTO POS AND HOLD. WE LANDED ON RWY 27R; AND WERE TOLD TO EXPEDITE TO THE NEAREST EXIT BECAUSE THERE WAS AN ACR MD80 ON 3 MI FINAL AND HE HAD SOMEONE IN POS TO HOLD. FEELING RUSHED; I TRIED TO HELP THE TWR OUT AS MUCH AS I COULD AS SAFETY WOULD ALLOW. ONCE WE SLOWED TO A SAFE SPD; I STARTED TO TURN THE ACFT TOWARD A HIGHSPD EXIT. IT WAS AT THIS POINT THE TWR CLRED THE TURBOPROP THAT WAS HOLDING FOR TKOF. I HAD TURNED A LITTLE TOO EARLY AND WAS CORRECTED BY MY FO WHO SAID THE EXIT WAS A LITTLE FURTHER UP. I IMMEDIATELY TOLD HIM TO NOTIFY THE TWR; WHICH HE DID; AND TELL THEM THAT WE WERE NOT CLR. THE TWR THEN QUERIED US AS TO IF WE WERE CLR OF THE RWY. I ANSWERED AND SAID NEGATIVE. HE THEN CALLED THE OTHER ACFT; BUT SAID NOTHING TO THEM. WE EXITED AT THE HIGHSPD TURNOFF AND THEN ANNOUNCED WE WERE CLR. THE ERRORS HERE STARTED WITH APCH. THEY SEQUENCED US ALL TOO CLOSE TOGETHER. ADD IN THAT THE TWR ASSUMED WE WERE CLR OF THE RWY INSTEAD OF REALLY LOOKING TO SEE. WE ADDED TO THE PROB BECAUSE WE TURNED TOO EARLY AND THE ACFT BEHIND US STARTED TO TKOF WITH US STILL ON THE RWY. THIS COULD HAVE BEEN A VERY DANGEROUS SIT.