FLT CREW OF CL65 INCUR LOSS OF SEPARATION WITH DEPARTING ACFT AFTER MAKING A GAR ON PARALLEL RWY.

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AFTER BEING CLRED TO LAND ON RWY 26R IN ATL; IT BECAME CLR THAT LNDG TFC (CPR KING AIR) AHEAD OF ME WOULD NOT CLR RWY 27R. OVER THE LNDG THRESHOLD FOR RWY 26R; ATL TWR ADVISED US TO 'GO AROUND; LNDG TFC AHEAD STILL ON YOUR RWY...CLB TO 3500 FT AND FLY RWY HDG.' WE COMPLIED AND READ BACK THE GAR CLRNC AS ISSUED. AN ACR B737 HAD SIMULTANEOUSLY BEEN CLRED FOR TKOF ON RWY 26L (THE PARALLEL RWY) AS WE DID THE GAR. I OVERHEARD HIS DEP CLRNC TO BE 'CLB 10000 FT; FLY HDG 330 DEGS.' THIS REGISTERED IN MY MIND AS AN IMMEDIATE AND DANGEROUS CONFLICT. I LOOKED L TO SEE THE B737 TURN TOWARDS OUR FLT PATH. I STARTED AN IMMEDIATE R TURN TO A 330 DEG HDG TO AVOID THE APCHING ACFT. ATL TWR SAW AND REALIZED THE CONFLICT AND IMMEDIATELY ISSUED B737 A 'FLY RWY HDG.' THE CONFLICT WAS RESOLVED BY OUR OWN ACTION AND BY THE QUICK INTERVENTION BY ATL TWR. AFTER LNDG IN ATL; I CALLED THE TWR SUPVR AND WE AGREED THAT BY NOT ISSUING A TKOF CLRNC WITH A R TURN UNTIL LNDG IS ASSURED ON THE PARALLEL RWY; WOULD PREVENT THIS FROM RECURRING. THERE WAS 'SOME CONFUSION' AS 'TO WHOM' THE ORIGINAL 330 DEG HDG WAS ISSUED. I'M CERTAIN THAT IT WAS ISSUED TO THE DEPARTING B737; AS THAT WAS THE HDG REQUIRED TO ACCIDENTALLY POINT HIM DIRECTLY TOWARDS ME. IN OUR BUSY ATC SYS; IT IS IMPORTANT TO KNOW YOUR OWN CLRNC; AND LISTEN AND KNOW WHAT YOUR TFC IS DOING OR ABOUT TO DO.