ACR X TCASII TA RA WITH Y NON ADHERENCE TO ATC CLRNC INSTRUCTION. EVASIVE ACTION CLB.

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ACR X PROCEEDING DSM DIRECT CAPITAL AT FL330 .80 MACH. X WAS ISSUED INSTRUCTIONS TO TURN R 30 DEGS FOR TFC. THE R TURN WAS INITIATED AND AT APPROX THE SAME TIME; TFC SHOWED ON MY TCASII SCREEN AT FL330 AND 7-8 MI AWAY. TCASII GAVE THE AURAL ADVISORY 'TFC; TFC.' THE TFC Y WAS AT 1 O'CLOCK AND I PICKED HIM UP VISUALLY. IT APPEARED OUR TURN WOULD CAUSE US TO PASS BEHIND THE TFC. AT THIS TIME A DIFFERENT CTLR TOLD US TO DSND TO FL310 AND AT THE SAME TIME; TCASII ISSUED AN RA TO 'CLB; CLB.' THE IVSI VISUALLY DIRECTED US TO CLB AND NOT TO DSND. I IMMEDIATELY BEGAN A CLB AND TOLD CTR WHAT I WAS DOING AND THAT I WOULD LATER COMPLY WITH HIS INSTRUCTIONS. I PASSED BEHIND THE TFC Y AND 400 FT ABOVE THE TFC; BASED ON MY TCASII PRESENTATION WHICH SHOWED THE TFC AT FL330 IN RED AND APPROX 2 MI TO MY L. AFTER THE CONFLICT WAS OVER; THE CTLR CLRED US DIRECT CAPITAL AND TO MAINTAIN FL330. I INQUIRED AS TO WHY WE WERE CO-ALT WITH ANOTHER ACFT AND WAS TOLD BY ZKC THAT WAS WHY WE WERE TOLD TO TURN 30 DEGS R AND THAT THERE WAS NEVER ANY CONFLICT. NOTE: THE TCASII AND CLR COMPANY POLICY TO FOLLOW TCASII ADVISORIES WERE VERY IMPORTANT IN THIS HIGH SPD CLOSURE SIT. I APPRECIATE THE ZKC CTLR FOR RECOGNIZING THE NEED FOR A TURN BUT I DO NOT UNDERSTAND WHY THE ACFT WERE ALLOWED TO GET SO CLOSE PRIOR TO CTLR ACTION. SUPPLEMENTAL INFORMATION FROM ACN 277498: THE CTLR (FEMALE VOICE) DIRECTED US TO TURN R 30 DEGS. A FEW SECONDS LATER TCASII GAVE US A TA AS WE STARTED OUR R TURN. WE PICKED UP THE TFC VISUALLY. A SECOND LATER ANOTHER CTLR (MALE VOICE) DIRECTED US TO DSND TO FL310 AND ABOUT THE SAME TIME WE GOT AN RA TO 'CLB; CLB.' WE CLBED AS DIRECTED BY THE TCASII (IN ACCORDANCE WITH PROCS FOR RA'S) TO FL334.