ZJX CTLR DESCRIBED LOSS OF SEPARATION AT FL360 WHEN PC12 WAS VECTORED FOR SEPARATION; BUT INITIATED A CLIMB BEFORE CLRNC WAS ISSUED.

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I WAS WORKING R49 SECTOR AT ZJX CTR; I NOTICED THAT I WAS GIVEN A 100 KT OVERTAKE FROM ZTL WITH AN ACR AND ACFT X (PC12). I THEN ASK THE ACR WOULD THEY BE ABLE TO ACCEPT FL380 FOR TFC. THEY SAID UNABLE; THAT THEY WERE TOO HVY. I THEN ASKED ACFT X IF THEY CAN ACCEPT FL380 FOR TFC. THE ACFT STATED YES AND ADVISED IT WOULD BE A SLOW CLB ABOUT 500 FPM. I SAID THAT IS FINE. I THEN TURNED ACFT X 20 DEGS L; VECTORS FOR YOUR CLB. I DID NOT ISSUE A CLB CLRNC BECAUSE I HAD ANOTHER ACR NBOUND AT FL370. SHORTLY THEREAFTER; ACFT X STARTED ITS CLB. WHEN I NOTICED THE ALT CHANGE; I IMMEDIATELY ASKED ACFT X; 'VERIFY LEVEL AT FL360.' ADVISED TO ACFT X THAT I DIDN'T ISSUE A CLB CLRNC AND TO MAINTAIN FL360. I THEN IMMEDIATELY TOLD THE ACFT Y TO TURN 30 DEGS R FOR TFC. THE PLT STATED THAT THE OTHER ACFT WAS APCHING RAPIDLY. I THEN TURNED ACFT X 30 DEGS R AND MAINTAIN FL360 RPT LEVEL. I WAS TRYING TO RE-ESTABLISH SEPARATION. THE ACFT Y SAID THAT HIS TCAS WENT OFF SO HE TOOK EVASIVE ACTION TO MANEUVER. AFTER FURTHER REVIEW FROM QUALITY ASSURANCE; IT WASN'T MY FAULT THEY CALLED IT A PLTDEV; BECAUSE I NEVER ISSUED A CLB CLRNC -- JUST A TURN TO VECTOR FOR ACFT X CLB. THEY ARE NOW PURSUING THE PLT. ALSO LOOKING AT THE REPLAY; ACFT Y NEVER TOOK THE 20 DEG L TURN; HE JUST DECIDED TO CLB INSTEAD.