A CTLR INSTRUCTOR COUNTERMANDED RADAR VECTOR INSTRUCTIONS ISSUED BY HIS TRAINEE BTWN A B727 AND ANOTHER UNKNOWN ACFT; WHICH WAS XING AND CLBING IN FRONT OF THE B727. CTLR ACTIONS WERE INSUFFICIENT TO STOP THE SYS ERROR.

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WHILE IN THE APCH CTL ENVIRONMENT IN BOI; WE WERE PROCEEDING DIRECT TO BOI VOR AT 13000 FT MSL. WE RECEIVED A TCASII TA FROM ACFT Y AND ALMOST SIMULTANEOUSLY RECEIVED A CALL FROM APCH CTL. BY THE NATURE OF THE XMISSIONS THERE SEEMED TO BE CTLR TRAINING IN PROGRESS. AT FIRST; INSTRUCTIONS WERE GIVEN TO TURN R (TOWARD TFC) THEN A SECOND VOICE COUNTERMANDED WITH A L TURN. WHEN TFC WAS FIRST SEEN ON TCASII; IT WAS IN A 12:30 O'CLOCK POS; 5 MI; 500 FT BELOW US AND CLBING. EVEN BEFORE APCH CTL STARTED; I INITIATED A TURN TO THE L. APCH CTL; AFTER INITIAL CALL TO TURN R; CHANGED INSTRUCTION (2ND CTLR) TO A L TURN. THE TFC PASSED ON OUR R SIDE ABOUT 2 MI (TCASII) AND APPARENTLY CONTINUED CLB THROUGH OUR ALT. WHEN I GOT ON THE GND; I CALLED APCH CTL VIA PHONE AND TALKED TO THE SUPVR. HE CONFIRMED THAT TRAINING HAD BEEN IN PROGRESS AND THAT AN ERROR HAD BEEN MADE BY THE STUDENT ISSUING A COMMAND TO TURN TO THE WRONG ACFT. TFC WAS NEVER SPOTTED VISUALLY BECAUSE OF IMC. NO RA WAS ISSUED BY TCASII.