INSTRUCTOR FAILS TO COMPLY WITH CTLR INSTRUCTIONS IN CLASS B AIRSPACE.

Narrative

5 MI W OF SEATAC; OVER MID VASHON ISLAND; I CALLED SEATTLE TWR AND REQUESTED AN EBOUND TRANSITION THROUGH THE CLASS B AIRSPACE. COMMON PROC: THE CTLR GIVES PLT A XPONDER CODE; IDENTS HIM ON RADAR; AND CLRS HIM TO CROSS THE APCH END AT 1500 FT MSL. I WAS MAKING THE RADIO CALLS; WHILE MY STUDENT WAS FLYING. TOGETHER WE HAVE DONE THIS ARPT XING ABOUT 50 TIMES. HE IS A KOREAN STUDENT WORKING ON HIS COMMERCIAL MULTI ENG RATING. ONCE WE WERE CLRED TO CROSS THE ARPT; HE NEGLECTED TO TURN TOWARDS THE APCH END. THE TWR QUERIED US ABOUT OUR INTENTIONS; 'SIR; ARE YOU GOING TO CROSS SEA-TAC OR BOEING?' I TOLD HER THAT I WAS PLANNING TO CROSS SEA-TAC AND THAT I REALIZED THAT I WAS A LITTLE FAR N. I HAD BEEN TELLING MY STUDENT TO TURN BACK TOWARDS SEA-TAC. HE DID SO; BUT VERY SLOWLY; THE TWR ASKED US 'DO YOU HAVE SEA-TAC IN SIGHT?' I TOLD HER I DID HAVE IT IN SIGHT. WE TURNED BACK IN TIME; BUT HAD WE CONTINUED WE WOULD HAVE BEEN IN CONFLICT WITH ARRIVING AIR TFC (AIRLINERS) INTO SEATAC. STUDENT ONLY MADE STANDARD RATE TURN; WHERE HE COULD HAVE STEEPENED THE BANK TO AVOID ANY CONFLICT.