B737 RESPONDS TO TCASII RA WITH C550 TFC IN HAVANA ARTCC RADAR AIRSPACE.

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IN THE VICINITY OF MAXIM INTXN; HAVANA CTR CALLED US AND IN UNUSUALLY BAD ENGLISH TOLD US TO TURN L TO A HDG OF 150 DEGS (COURSE WAS APPROX 240 DEGS). NO 'IMMEDIATE' CALL OR OTHER INDICATION OF CONCERN EVIDENT. SOME INITIAL CONFUSION AS TO CALL FROM HAVANA BECAUSE OF POOR ENGLISH. STARTED L TURN TO REQUESTED HDG WHEN I NOTED A POP-UP TCASII TARGET AT 12 O'CLOCK POS; 7 MI; CO-ALT. ALMOST IMMEDIATELY; WE GOT A TA. THIS TARGET WAS NEVER CALLED OUT TO US BY HAVANA. WITHIN 10 SECONDS; WHILE IN THE TURN; NOW A BIT MORE AGGRESSIVE; WE RECEIVED AN RA WITH A CLB CALL. COMPLIED WITH RA AND NOTIFIED HAVANA. AS TARGET CLOSED TO WITHIN A MI OR SO; WE FINALLY SAW IT BEGIN TO DSND ON THE TCASII. ALTHOUGH WE NEVER ACTUALLY SAW THE TARGET (CLR SKIES); I ESTIMATE WE PASSED WITHIN 1/4 MI HORIZLY (OUR R SIDE) AND 600 FT VERTLY (BASED ON TCASII INFO). HAVANA CTR WAS VERY RELUCTANT TO PROVIDE US ANY INFO ABOUT THE INCIDENT; BUT WE FINALLY WERE TOLD IT WAS A HONDURAN REGISTERED CITATION 5 WHO WAS DSNDING TO FL330. HAVANA GAVE NO FEEDBACK AS TO WHY THIS OCCURRED AND; TO BE HONEST; NEVER SEEMED CONCERNED. AT NO TIME DID THEY POINT OUT THAT ACFT. IN ADDITIONAL; ALTHOUGH I WAS NOT SPECIFICALLY SCANNING THE NAV DISPLAY AT THE TIME; NEITHER OF US NOTED A TCASII TARGET AT ALL UNTIL WE BEGAN THE TURN.