A319 FLT CREW IS INSTRUCTED TO 'TURN IMMEDIATELY' AND DESCEND FOLLOWING A CLRNC TO CLIMB.

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WE WERE GIVEN A CLB FROM FL190 TO FL230 FROM ZJX. AS WE WERE CLBING THE CTLR ASKED US TO STOP THE CLB AT FL210 AND WE DID. JUST AS WE LEVELED AT FL210 AND CTLR RECLRED US TO FL230. WE ACKNOWLEDGED HIS CLRNC AND STARTED CLBING TO FL230. AS WE PASSED THROUGH FL216 THE CTLR TOLD US TO MAINTAIN FL210 AND TURN R 30 DEGS. IT WAS AT THIS TIME WE RECEIVED A TFC ALERT FROM OUR TCAS. THE ALERT NEVER PROGRESSED TO AN RA. WE NEVER HAD VISUAL CONTACT WITH THE OTHER ACFT. SHORTLY AFTER WE LEVELED BACK OFF AT FL210 THE CTLR CLRED US BACK ON COURSE AND RECLRED US TO FL230. WE DETERMINED AN EVENT HAD OCCURRED WHEN THE CTLR TOLD US TO TURN R IMMEDIATELY 30 DEGS AND MAINTAIN TO FL210. AT ABOUT THE SAME TIME THE CTLR ISSUED HIS INSTRUCTIONS THE TCAS SAID TFC; TFC. ALSO WE HEARD THE OTHER ACFT RPT THAT THEY HAD US IN SIGHT. WHEN THE FREQ IS VERY BUSY AS IT WAS; MAYBE USING A SHORTER RANGE ON THE ND SCALE TO DISPLAY TFC BETTER IN RELATION TO YOUR ACFT SO IF CLB OR DSCNT IS GIVEN THAT SEEMS QUESTIONABLE YOU COULD QUERY THE CTLR TO MAKE SURE THAT IS WHAT THEY WANT AND YOU ARE THE ACFT THEY ARE TALKING TO.