C130 CAPT LEARNS THAT HE DID NOT FOLLOW GAR INSTRUCTIONS RESULTING IN A CONFLICT WITH A T43 MAKING AN APCH TO THE OPPOSITE END OF THE RWY WITH THE OPTION TO MAKE A MISSED APCH.

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I (C130) WAS CLRED FOR AN ILS TO RWY 13 ON AN IFR CLRNC. AFTER BEING SWITCHED OVER TO TWR AND APPROX 500 FT AGL; I WAS GIVEN CLRNC TO TURN OFF OF THE APCH DUE TO A T43 LNDG OPPOSITE DIRECTION TO RWY 31. HE WAS CLRED THE OPTION. MY INSTRUCTIONS WERE TO TURN L TO CIRCLE W TO RWY 31 WHICH IS NOT POSSIBLE SINCE L WAS E OF THE FIELD. AN INSTRUCTOR CTLR OR TWR SUPVR (I'M NOT SURE WHICH) CORRECTED THE INITIAL INSTRUCTION BY TELLING ME TO TURN R CIRCLE W OF THE FIELD. THESE INSTRUCTIONS MADE SENSE AND WERE SUPPORTED BY THE FACT THERE WAS ANOTHER C130 IN THE PATTERN TO THE W FOR RWY 31. I WAS IN A SIMULATED 3-ENG CONFIGN WITH #4 SIMULATED SHUTDOWN. MY STUDENT INITIATED A GAR BY BANKING L 5 DEGS WHILE I FED-IN THE #4 ENG AND TERMINATED THE SIMULATED EMER THEN TURNED R. WE ACKNOWLEDGED TO ATC THAT WE WERE IN THE TURN AND THAT TURN WAS PLOTTED WITH RADAR TO BE 1.5 MI FROM THE RWY. NOTHING ELSE WAS SAID FOR ABOUT 1 HR UNTIL THE T43 WAS DEPARTING THE PATTERN FOR GOOD. THE T43 ASKED THE CTLR ABOUT THE CONFLICT HE HAD WITH THE C130 AND THE CTLR WAS UNAWARE OF THE SIT THE T43 WAS REFERRING TO. AFTER I LANDED THE OTHER PLT (T43) CALLED ME TO SEE IF I HAD SEEN ANY CONFLICT. HIS CONCERN WAS THAT HE WAS CLRED THE OPTION AND THAT HIS FLT PATH MIGHT HAVE BEEN A CONFLICT WITH ME. HOWEVER; I SAW NO IMMEDIATE CONFLICT SINCE I WAS AROUND 500 FT AGL AND 1.5 MI FROM THE RWY. HE CLAIMED HE WAS GOING TO FILE A HATR AGAINST ATC. ATC CALLED ME THE NEXT DAY ADVISING ME THE TAPES HAD BEEN PULLED AND A HATR FILED AGAINST THEM. THEY ALSO STATED THAT THEY HAD GIVEN ME A THIRD CLRNC ON MY GAR TO FLY E OF THE FIELD. MY CREW WAS UNAWARE OF THAT CLRNC. OUR PERCEPTION IS THAT NO IMMEDIATE CONFLICT EXISTED. HOWEVER; ON THE ILS OUR POS TO THE T43 IS BEAK-TO-BEAK SINCE THE ILS COURSE POS THE ACFT TO THE 12 O'CLOCK POS. CONFUSING CLRNCS BY MULTIPLE CTLRS MAY NOT HAVE HELPED PERCEPTIONS; AND TURNING US E OF THE FIELD WOULD HAVE PUT US IN CONFLICT WITH TFC ON BASE LEG FROM THE W. WE FELT OUR COURSE OF ACTION TO BE CORRECT AT THE TIME; BASED ON WHAT WE HEARD; AS WELL AS THE SAFEST DUE TO OTHER TFC IN THE AREA.