GLF2 FLC INITIATE EVASIVE MANEUVER TO AVOID ANOTHER ACFT WHILE DSNDING FROM ZSU INTO TNCM CTLED AIRSPACE.

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ON DSCNT INTO TNCM AT APPROX XA55Z; XXXX; ZSU CLRED US TO 15000 FT. WHEN WE WERE AT 15000 FT; ZSU TOLD US TO CONTACT JULIANA APCH ON 118.7. AFTER CONTACT WITH JULIANA; JULIANA CLRED US TO 2500 FT (WE ASKED IF THAT WAS 1500 FT OR 2500 FT AND JULIANA SAID 2500 FT) AT WHICH TIME WE WERE CLRED FOR VISUAL APCH TO RWY 9. THE DSCNT FROM 15000 FT TO 2500 FT CAUSED A CONFLICT WITH AN ACFT UNDER SAN JUAN CTL; AND WE CROSSED OVER THE TOP OF THIS ACFT AT APPROX 2000 FT AND 5 MI. I WAS REQUESTED TO CONTACT ZSU AFTER WE LANDED. ZSU ADVISED ME THAT JULIANA ALLOWED US TO DSND TOO EARLY; CAUSING THE CONFLICT WITH OTHER ACFT. JULIANA ADVISED SAN JUAN THAT ACFT Y ADVISED OF NO RESTRS UPON CONTACT. BUT XXXX HAD NO RESTRS OTHER THAN CLRED FROM 15000 FT TO 2500 FT. SUPPLEMENTAL INFO FROM ACN 535473: DURING THE DSCNT; WE NOTICED AN ACFT ON TCASII 2000 FT BELOW US. ABOUT 10 MI IN FRONT OF THE ACFT ON TCASII WE DSNDED THROUGH HIS ALT. AT THAT TIME JULIANA ASKED US TO CALL ZSU AGAIN. ZSU TOLD US THAT WE WERE NEVER CLRED TO DSND BELOW 15000 FT. I REPLIED THAT WE WERE HANDED OFF TO JULIANA AND THEY GAVE THE CLRNC BELOW 15000 FT. SAN JUAN SAID THAT WE TOLD JULIANA THAT WE WERE 'UNRESTR;' THEN TOLD US TO CALL THEM ONCE WE WERE ON THE GND. WE CONTACTED JULIANA AND ASKED THEM WHAT THEY THOUGHT HAD HAPPENED. JULIANA REPLIED THAT WE HAD CHKED IN ON THE INITIAL CALL AT 15000 FT AND NO RESTRS. THAT STATEMENT IS NOT TRUE. I BELIEVE THAT JULIANA GAVE US A DSCNT CLRNC BY MISTAKE AND WHEN SAN JUAN ASKED THEM ABOUT OUR DSCNT; JULIANA TRIED TO BLAME US.