ZJX CTLR PROVIDING OJT EXPERIENCED LOSS OF SEPARATION AT FL307 DURING WX DEV MANEUVERS WHEN ACR WAS SLOW TO RESPOND TO CORRECTIVE INSTRUCTIONS.

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I WAS PROVIDING TRAINING (RADAR TRAINING) AT R58; SAINT AUGUSTINE SECTOR. WX WAS IMPACTING THE SECTOR; CAUSING NUMEROUS DEVS. THE SECTOR FEEDING US WAS ALLOWING THE ACFT TO DEVIATE BOTH E AND W AROUND THE CELL AND THEN CONVERGE S OF THE CELL. I ASKED FOR A D-SIDE; BUT ONE WAS NOT PROVIDED UNTIL AFTER THE SITUATION. WHEN ACR Y CHKED IN; I NOTICED THE CONVERGENCE WITH ACR X. THE TRAINEE ISSUED A CLRNC FOR ACR X TO 'MAINTAIN 310.' THE PLT READ BACK 'ROGER; 310 KTS.' I THEN TOOK OVER THE POS AND CLRED THE ACR X TO 'FLY HDG 120 DEGS; MAINTAIN FL310.' ACR X ROGERED THE CLRNC. I DSNDED THE ACR Y FROM FL300 TO FL280. AFTER SCANNING THE REST OF THE SECTOR; I NOTICED THAT THE ACR X WAS NOT TURNING AS CLRED. I ISSUED A TURN TO ACR Y TO MAINTAIN THE SEPARATION. AFTER LISTENING TO THE TAPES; I REALIZED THE ACR X TOOK APPROX 1 MIN TO BEGIN HIS TURN. ON FREQ; HE RPTED LEVELING FL310 AND COMMENCING A TURN TO A 120 DEG HDG. HAD ACR X TURNED WHEN CLRED; THE SEPARATION BTWN HIM AND ACR Y WOULD HAVE BEEN MAINTAINED. SUPPLEMENTAL INFO FROM ACN 713392: I ASKED ZJX FOR A R DEV FOR A BUILD-UP AHEAD. THE 10 DEG DEV TO THE R WAS APPROVED. AS WE WERE GOING AROUND THE BUILD-UP; WE WERE ISSUED A DSCNT TO FL260. I READ THE CLRNC BACK AND ASKED HIM TO VERIFY THE DSCNT TO FL260 AND RE RESPONDED 'ROGER; 260.' (THE DSCNT WAS EARLIER THAN EXPECTED.) WE STARTED THE DSCNT. PASSING FL305; ANOTHER CTLR TOOK OVER AND ISSUED FL310 AND A L TURN TO A 120 DEG HDG. I READ BACK THE CLRNC AND VERIFIED IT AGAIN. THE CTLR CONFIRMED FL310 AND A 120 DEG HDG. WE CLBED BACK TO FL310 AND TURNED TO A HDG OF 120 DEGS.