THE FLT PATHS OF 2 ACFT CONFLICTED DURING SIMULTANEOUS DEPS; FROM PARALLEL RWYS.

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WE WERE OPERATING AS (COMPANY CALL; FLT #) TO ATHENS; GA. WE WERE GIVEN A TKOF CLRNC FROM CHARLOTTE TWR AND WE WERE ASSIGNED A R TURN TO 270 DEG AFTER TKOF. WE WERE DEPARTING ON RWY 18L. TWR DID NOT ADVISE US OF TFC DEPARTING ON RWY 18R. WE DEPARTED RWY 18L; AND AFTER PASSING THROUGH 400 FT; WE STARTED A R TURN TO A 270 DEG HDG. WHILE IN THE TURN; TWR ADVISED US OF TFC DEPARTING RWY 18R (A FOKKER 100) AND THAT WE WOULD PASS BEHIND HIM. WHEN I TURNED TO LOOK FOR THE TFC; I COULD SEE THAT HE WAS WELL BEHIND US AND THAT IF WE CONTINUED OUR TURN; WE WOULD BE HDG STRAIGHT AT HIM. I IMMEDIATELY STARTED A TURN BACK TO THE L AND AT THE SAME TIME; OUR TCASII COMMANDED A CLB AND WE COMPLIED. IT SHOULD BE NOTED TOO; THAT MY CAPT NEVER SAW HOW CLOSE WE WERE. WE MISSED HIM BY APPROX 200 FT. I FEEL THAT THIS WAS A CTLR ERROR AND AFTER THE OCCURRENCE; CTLR EVEN SAID THAT FROM THE TWR; IT LOOKED AS IF WE WOULD PASS BEHIND THE JET. I ALSO FEEL THAT SOME TYPE OF ADDITIONAL MEASURES SHOULD BE TAKEN BY CTLRS TO PREVENT THIS TYPE OF OCCURRENCE; BECAUSE WE WOULD NOT SEE THE JET UNTIL WE WERE IN THE TURN. SUPPLEMENTAL INFO FROM ACN 296991: IN TURN AT APPROX 500 FT AGL; TWR ADVISED TFC A (ACR NAME) HAD DEPARTED RWY 18R AND WE WOULD PASS BEHIND HIM. (AT THIS POINT WE WERE STILL E OF RWY 18R) AND THAT HE WOULD BE NO FACTOR; WE SPOTTED TFC AT 1:30 TO 2 O'CLOCK LOW AND CLBING. AT THIS POINT WE DECIDED THAT A CONFLICT EXISTED AND AN EVASIVE TURN WAS MADE TO THE S TO AVOID TFC. AFTER TFC WAS CLR WE TURNED BACK TO 270 DEG HDG. TFC ON RWYS 18L AND 18R IN CLT IS HANDLED BY 2 DIFFERENT AIR TFC POS.