ACR X HAD NMAC WITH VFR SMT Y. ACR X TCASII RA EVASIVE ACTION TAKEN FROM SMT Y. SEE AND AVOID.

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ON-THE-JOB TRAINING WAS BEING CONDUCTED ON THE HAMMOND LOW ALT SECTOR. ACR X WAS NBOUND OUT OF NEW ORLEANS; LA. WHEN HE CALLED CTR; HE WAS NWBOUND TURNING SLOWLY TO A 350 DEG HDG; OUT OF ABOUT 8000 CLBING TO 15000. SMT Y WAS EBOUND ALONG V70 CLBING VFR. (WE WERE PROVIDING VFR FLT FOLLOWING.) THE RADAR TRAINEE AND I THOUGHT ACR X WOULD PASS BEHIND SMT X. ACR X WAS ADVISED OF THE TFC AND CLBED TO FL230. HE ACKNOWLEDGED IT. THEY WERE APPROX 15 MI APART. I BECAME AWARE THAT THERE WAS GOING TO BE A PROBLEM WHEN ACR X STOPPED HIS TURN AND WAS CONVERGING WITH SMT Y AT A 90 DEG ANGLE. I HESITATED; THINKING THE RADAR TRAINEE WOULD RESOLVE THE SITUATION. SMT Y WAS CLBING THROUGH 11300 FT WHEN I ASKED HIM IF HE WAS STOPPING AT 11500 FT. THE REPLY WAS 'NEGATIVE; CLBING TO 13500 FT.' THE ACR WAS OUT OF ABOUT 11200 FT. I TOLD THE VFR TO STOP HIS CLB AND CALLED TFC TELLING HIM ACR X; WHO WAS CLBING FASTER; WOULD CLB ABOVE HIM. AT THIS POINT; I'M NOT SURE WHAT HAPPENED BUT AFTER THE TARGETS SEPARATED; ACR X WAS BELOW SMT Y. I TOLD ACR X TFC WAS NO LONGER A FACTOR. HE SAID 'I KNOW WE HAD HIM ON TCASII. SMT Y SAID NOTHING. THIS IS THE RADAR STUDENT'S FIRST RADAR SECTOR WITH ABOUT 90 OF THE ALLOTTED 120 HRS. THE SECTOR WAS MODERATELY BUSY AND HE WAS AWARE OF THE SITUATION. I WAITED TOO LONG FOR HIM TO RESOLVE IT. A 20 DEG TURN TO THE L; WHEN THEY WERE 1 1/2-2 MINS APART WOULD HAVE RESOLVED THE SITUATION. WHEN QUESTIONED; THE STUDENT THOUGHT HE WAS NOT REQUIRED TO TAKE ACTION AFTER TFC WAS ISSUED; UNLESS THE PLT REQUESTED IT. IF THE PLT OF ACR X WAS RESPONDING TO A TCASII RESOLUTION; DSNDING TO AVOID; THE SITUATION BECAME MORE DANGEROUS BECAUSE I TOLD SMT Y TO STOP CLBING.