DUE TO SLOWER DEPARTING TFC; IT WAS NECESSARY FOR DEP CTL TO INTERVENE AND TURN A DEPARTING LTT CLBING UP FROM BEHIND THE SLOWER ACFT.

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WE WRE CLRED FOR TKOF ON RWY 10 AT SJT; SOON AFTER A CARAVAN DEPARTED. NORMALLY; BEFORE THEY CLR US FOR TKOF BEHIND A SLOWER ACFT; THEY ASK IF WE HAVE HIM IN SIGHT. TODAY THEY DID NOT; THEY JUST CLRED US FOR TKOF. UPON REACHING 400 FT; WHICH IS THE MSA FOR MANEUVERING AS PER OUR COMPANY OPS MANUAL; WE PROCEEDED TO TURN TO 075 DEG HDG; WHICH WAS THE HDG ASSIGNED IN OUR CLRNC. WHEN WE WERE APPROX 1000 FT ON THE 075 DEG HDG; ATC INSTRUCTED US TO MAKE AN IMMEDIATE L TURN TO 360 DEGS AND INFORMED US THAT THIS WAS A TA AND TOLD US WHERE THE TFC WAS. AT THAT POINT I SPOTTED THE ACFT AND CALLED HIM IN SIGHT. AS WE EVASIVELY TURNED TO 360 DEGS; THE CAPT; WHO WAS THE PF; NEVER SAW THE ACFT. WHEN WE RETURNED FROM OUR TRIP WE WERE INFORMED TO CALL THE TWR. THEY SAID WE WERE NOT ON THE ASSIGNED HDG. I KNOW FOR A FACT WE WERE ON THE CORRECT HDG BECAUSE I WAS MONITORING THE CAPT. THEY THEN PROCEEDED TO DISCUSS CERTIFICATE ACTIONS AGAINST US. I THINK THE PROB LIES WITH EITHER THE TWR CTLR LAUNCHING US TOO EARLY OR THE APCH CTLR NOT REALIZING THE DIFFERENCE IN AIRSPD OF OUR ACFT. WE COULD NOT SEE THE TFC DUE TO SOME SCATTERED CLOUDS BTWN US AND HIM UNTIL ATC POINTED IT OUT TO US AND I CAUGHT HIM OUT OF THE CORNER OF MY EYE AS WE PROCEEDED TO TURN.