DHC8 OVERSHOOTS CLRNC AND CONFLICTS WITH CARJ WHILE UNDER IAD CTL.

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ACTING AS CIC; DEP SECTOR CALLED ME OVER TO BE RELIEVED FOR A POSSIBLE PLTDEV. DH8 ON STAR; RJ ON VECTORS. APPARENTLY; DH8 WAS SLIGHTLY OFF COURSE. CTLR CAUGHT IT AND TOOK ACTION AS SOON AS SHE WAS AWARE THE DH8 WAS OFF COURSE. SUPPLEMENTAL INFO FROM ACN 521820: WE WERE ON THE MANNE 4 ARR INTO DCA. CLRNC WAS GIVEN TO GO DIRECT TO MANNE INTXN; APPROX 060 DEG HDG; AND RESUME THE ARR. PRIOR TO REACHING MANNE; I HAD SELECTED THE HDG MODE ON THE AUTOFLT CTLR; ALSO SELECTED VOR TO SET UP FOR THE APCH IN USE AT DCA. WHEN I RESELECTED THE FMS; I DIDN'T SELECT THE NAV MODE AGAIN; SO WHEN PASSING THE MANNE INTXN; REMAINED ON THE 060 DEG HDG. I NOTICED THIS WHEN WE WERE 1.8 MI PAST THE COURSE (1.8 MI NE OF COURSE) AND TURNED TO 150 DEG HDG TO REJOIN THE ARR COURSE. JUST AFTER I STARTED THE TURN; THE APCH CTLR TOLD ME TO TURN TO 180 DEG HDG. THE CTLR REPEATED THIS COMMAND SAYING IT WAS FOR TFC. THE COPLT DURING THIS WAS ON ANOTHER RADIO CHKING IN WITH DCA OPS. THE COPLT HEARD OUR TCASII SYS GIVE A TFC ALERT AND STATED TO ME THAT TFC WAS NO CLOSER THAN THE 2 MI RING ON OUR TCASII PANEL AND WAS 1100 FT ABOVE. WE DID NOT GET AN RA ONLY A TFC ALERT; AND TURN COMMANDED FROM ATC.