ATC HAD NMAC LESS THAN STANDARD SEPARATION BETWEEN ARR DEP MLG ACFT AFTER RWY CHANGE; LACK OF COORD AND ACFT UNDER SEPARATION ATC JURISDICTION.

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MLG X DEPARTED PIT RWY 10R WITH A RIGHT TURN S. MLG Y WAS ON AN ILS APCH TO RWY 32; 20 MI FINAL. BECAUSE OF INCOMPLETE COORD; DEP THOUGHT MLG Y WOULD MAINTAIN 6000' WHILE MLG X TUNNELED UNDERNEATH AT 5000'. ACTUALLY; MLG Y WAS CLRED FOR THE APCH AND BOTH ACFT OCCUPIED SAME AIRSPACE AT 4000' 6 MI SE PIT. THIS HAPPENED AS WE WERE CHANGING LNDG DIRECTIONS FROM RWY 10R TO 32. MLG X WAS LAST DEP OFF 10R AND MLG Y WAS FIRST ARR ON R32. BOTH CTLRS REALIZED WHAT WAS TAKING PLACE AND ATTEMPTED CORRECTIVE ACTION; BUT IT WAS TOO LATE. I BELIEVE IT WAS CAUSED BY 3 OR 4 CONTRIBUTING FACTORS: DEP SHOULD HAVE PARALLELED THE COURSE OF THE ARR UNTIL POSITIVE MLG Y WOULD LEVEL AT 6000'. YOU DON'T VECTOR AN ACFT RIGHT AT ANOTHER UNDER THOSE CONDITIONS. CTLR IS PRACTICALLY BRAND NEW--QUALIFIED 1 MONTH. APCH SHOULD NOT HAVE CHANGED MLG Y TO TWR WITH APCH CLRNC UNTIL SEEING WHAT DEP WAS GOING TO DO WITH MLG X. SUPVR COULD HAVE BEEN MORE POSITIVE IN TELLING EACH CTLR WHAT TO DO. I DIDN'T BECAUSE I ASSUMED TELLING PEOPLE ABOUT 2 ACFT 20 MI APART WAS SUFFICIENT WARNING FOR THEM TO BE KEPT AWAY. SUPPLEMENTAL INFO FROM ACN 92110: OUT OF APPROX 2000' WE WERE GIVEN A CLRNC TO FLY HDG 200 DEGS; CLB TO 4000' AND CONTACT DEP. DEP CLRED US TO 5000'. OUT OF 4170 DEP TOLD US TO MAINTAIN 4000'. AFTER REACHING A MAX ALT OF 4300'; I LEVELED AT 4000'. APPROX 15 SECS AFTER LEVELING AT 4000' I SAW THE CONFLICTING ACFT AT ABOUT 11 O'CLOCK; LEFT TO RIGHT; ON A COLLISION COURSE. I MADE AN IMMEDIATE EVASIVE LEFT TURN. THE CONFLICTING ACFT (ALSO A COMPANY MLG Y) MADE A SIMULTANEOUS EVASIVE TURN TO THE LEFT. AS WE WERE IN THE EVASIVE TURNS; DEP CTL CALLED OUT 12 O'CLOCK TFC; 3 MI. THE CAPT CALLED PIT DEP FROM TAMPA ON THE LANDLINE. THE SUPVR INDICATED TO HIM THAT THERE HAD BEEN A CTLR ERROR AND THAT IT WAS 'UNDER INVESTIGATION.' THE SUPVR TOLD THE CAPT THAT THEIR (ATC) EQUIPMENT INDICATED 300' SEP. SUPPLEMENTAL INFO FROM ACN 91276: AT APPROX 4000' MSL TWR INSTRUCTED US TO CLB IMMEDIATELY TO 5000'; THAT WE HAD TFC OFF OUR RIGHT SIDE. AT THIS TIME THE COPLT; WHO WAS FLYING THE ACFT; AND I SAW THE TFC (LATER IDENTED AS MLG X) APPROX 500' VERT AND 800' HORIZ TO OUR RIGHT IN A LEFT CLBING TURN AWAY FROM US. WE WERE ORIGINALLY BEING VECTORED FOR RWY 10R BUT WERE REASSIGNED RWY 32. SUPPLEMENTAL INFO FROM ACN 91794: APPARENTLY MLG X HAD JUST DEPARTED RWY 10R BEFORE THEY CHANGED RWYS AND WAS GIVEN A DEP THAT CROSSED THE APCH PATH TO RWY 32. THE ONLY TFC ADVISORY WE WERE GIVEN WAS WITH THE IMMEDIATE CLB INSTRUCTION.