AN A320 DEPARTING MDPC EXPERIENCED A TFC CONFLICT WITH AN ARRIVING ATR72; PERHAPS BECAUSE THE A320 MISSED A CLRNC FOR A TURN AFTER TKOF.

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AFTER A LENGTHY GND DELAY FOR SUPPORT EQUIP AND MECHANICAL PROBS; WE TAXIED OUT FOR TKOF. WE RECEIVED A CLRNC TO CLB TO FL340 AND A DEP FREQ. WE THOUGHT THAT IT WAS ODD THAT THERE WAS NO INTERMEDIATE LEVELOFF ALT; BUT I FIGURED IT WAS JUST THE WAY IT WAS DONE FROM AN ISLAND ARPT. AFTER TKOF; WE SWITCHED TO THE FREQ ONLY TO FIND OUT THAT IT WAS THE WRONG FREQ. WE WERE DIRECTED TO THE CORRECT DEP FREQ AND THE CAPT CHKED IN PASSING THROUGH ABOUT 1000 FT. THE CTLR TOLD US TO STAND BY. PASSING ABOUT 2700 FT; WE GOT A TCAS ADVISORY. I LOOKED DOWN TO SEE A TARGET AT OUR 1 O'CLOCK POS; 3 MI AND 300 FT ABOVE OUR ALT. THE CAPT DIRECTED AN IMMEDIATE LEVELOFF AND HELPED ME WITH THE PUSH OVER (HE SAW THE TARGET A LITTLE SOONER THAN I DID AND SAW THE NEED A LITTLE SOONER THAN I). WE LEVELED OFF ABOUT 3000 FT AND ABOVE THE UNDERCAST WITH ANOTHER LAYER ABOVE. THE TARGET SLOWLY DRIFTED TO OUR R AND THE ALT DIFFERENCE STARTED TO INCREASE. SHORTLY THEREAFTER; I SAW A TURBOPROP BREAK OUT AT 3 O'CLOCK POS ABOUT 1500 FT ABOVE US AND A COUPLE OF MI AWAY. WE LISTENED TO THE RADIO AS THE PLT ARGUED WITH THE DEP CTLR ABOUT HIS CLRNC. IT SOUNDED LIKE HE HAD BEEN TOLD TO HEAD TO THE VOR AND THEN ENTER A R DOWNWIND (THE FIELD WAS IFR). THE CTLR TOLD HIM HE WAS TO HAVE LEVELED OFF AT 4000 FT WHILE THE TURBOPROP PLT SAID THEY GOT THAT CALL AS THEY WERE DSNDING THROUGH 3500 FT. EVERYBODY WAS CONFUSED AND IRRITATED. THE CTLR TOLD US TO MAINTAIN 3000 FT; WHICH WE DID UNTIL WE WERE SEVERAL MI E OF THE AREA AND THEN FINALLY GOT A CLB AND A TURN BACK NBOUND. THE CAPT AND I WERE BOTH VERY SURE WE HAD NO ALT INSTRUCTIONS FOR DEP OTHER THAN FL340 BECAUSE WE BOTH REMARKED ABOUT IT AT THE TIME WE GOT THE CLRNC. THE FACT THAT WE WERE ALSO GIVEN THE WRONG DEP FREQ (I THINK IT WAS ACTUALLY THE SANTO DOMINGO FIR FREQ) MAKES ME THINK THERE WAS SOMETHING WRONG WITH THE CLRNC WE RECEIVED WHILE ON THE GND. LOOKING BACK; WE SHOULD HAVE QUERIED THE CTLR ABOUT OUR CLRNC WHEN WE GOT IT; SINCE THE INITIAL ALT ASSIGNMENT SEEMED ODD. MAYBE THAT WOULD HAVE SURFACED THE PROB WITH THE CLRNC. AT THE TIME WE WERE ALREADY LATE; HOT; TIRED; SWEATY; AND IRRITATED (THE AIRPLANE WAS SENT TO THE TROPICS WITH NO APU) AND JUST WANTED TO LEAVE. THAT'S NO EXCUSE; BUT WAS PROBABLY A FACTOR AND; THEREFORE; SHOULD HAVE BEEN A RED FLAG. NEXT TIME I WILL ASK MORE QUESTIONS EVEN IF I CAN'T UNDERSTAND THE CTLR. SUPPLEMENTAL INFO FROM ACN 705065: DURING APCH INTO MDPC; AFTER PASSING ANTEX INTXN AT 6000 FT; ATC CLRED US TO 3000 FT AND TO FLY DIRECT TO MDPC AND EXPECT R TFC FOR RWY 9. CLRNC WAS READ BACK AND WHEN PASSING 3700 FT ATC CALLS; IN SPANISH; FOR US TO MAINTAIN 4000 FT DUE TO OPPOSITE DIRECTION TFC CLBING TO 3000 FT. ONLY FOR MY SPANISH SPEAKING FO DID WE HEAR THIS INSTRUCTION. ATC REPEATED THE INSTRUCTION AGAIN IN ENGLISH; AFTER WE BEGAN A CLBING L TURN DUE TO THE TCAS DISPLAY SHOWING TFC DIRECTLY IN FRONT OF US AND APPROX 500 FT BELOW. NEVER ACQUIRED A VISUAL ON THE TFC. AFTER CLR OF TFC; PROCEEDED TO MDPC AND LANDED WITHOUT FURTHER INCIDENT. SPOKE TO THE CTLR ON THE PHONE IN MDPC AND HE WAS SORRY FOR THE INCIDENT. SAID THAT THE OTHER ACFT WAS AN ACFT WHICH DEPARTED MDPC AND WAS CLRED TO 3000 FT WITH A L TURN OUT ON COURSE. SEEMS THE OTHER ACFT MAINTAINED RWY HDG AND THUS CREATED THE NEAR MISS. I ADVISED THE CTLR THAT IT SEEMS VERY BAD PROC TO CLR 2 ACFT TO THE SAME ALT IN SUCH CLOSE PROX. HE AGAIN SAID SORRY AND SAID THEIR RADAR IS 'SPOTTY' AT TIMES AND HE DIDN'T SEE THE CONFLICT SOON ENOUGH TO AVOID THE TCAS ALERT. ADVISED ATC THAT WE WOULD FILE A RPT ON THE INCIDENT. HANDLING ERROR: COM. REACTION: IMMEDIATE CLBING TURN TO AVOID TFC CONFLICT SHOWN ON TCAS.