ATC CTLR GAVE EVASIVE ACTION TURN TO AN MLG ACR ACFT TO AVOID ANOTHER ACFT CONVERGING AT THE SAME ALT.

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WE WERE ON THE DADES ARR INTO TPA APCHING DADES; LEVEL AT 13000 FT AND JUST TURNED OVER TO TPA APCH CTL. THE APCH CTLR CLRED US TO 10000 FT. THE FO STARTED A 1000 FPM DSCNT. WHEN WE WERE PASSING 10700 FT; THE CTLR ASKED OUR ALT. AS I RESPONDED; HE TOLD US TO TURN R TO 250 DEGS REF TFC IN OUR 12 O'CLOCK APPROX 7 MI. THE FO WHO HAD BEEN MONITORING THE TFC VIA TCASII BEGAN AN IMMEDIATE 30 DEG BANK TURN TO THE NEW HDG WHILE I LOOKED FOR THE TFC. AT THE COMPLETION OF THE TURN; TCASII INDICATED THE TFC WAS APPROX 3 MI OFF OUR L WING. AT ABOUT THAT TIME; TCASII DECLARED A TA WHICH WAS SUBSEQUENTLY TURNED INTO AN RA INDICATING A 500 FPM DSCNT. BY THAT TIME; WE WERE LEVEL WITH OUR CLRNC ALT OF 10000 FT. WE HAD ALREADY RECEIVED A TURN FROM APCH CTL REF THE TFC AND WERE COMPLYING WITH THE EXISTING CLRNCS EXACTLY. THE CTLR HAD NOT MADE ANY FURTHER REF TO THE TFC AND THE APPEARANCE WAS THAT EVERYTHING WAS UNDER CTL FROM THE CTLR'S POINT OF VIEW. BY THE TIME THE RA WAS ANNOUNCED BY TCASII; THE TFC WAS BEHIND OUR L WING AND DIVERGING. THE FO WAS TAKING ALL THIS INTO ACCOUNT AND MOMENTARILY DELAYED REACTING TO THE RA; SINCE IN HIS JUDGEMENT THE POSSIBILITY OF A NEAR MISS WAS NOW NON-EXISTENT. BY THE TIME I LOOKED BACK AT THE INSTS AND REALIZED THAT THE FO HAD NOT REACTED TO THE RA; TCASII ANNOUNCED CLR OF CONFLICT. ALL THIS TOOK ONLY A FEW SECONDS. THE REST OF THE FLT INTO TPA WAS UNEVENTFUL. AFTER WE ARRIVED AT THE GATE; I ASKED THE FO WHY HE HAD NOT RESPONDED TO THE RA. HE REPLIED THAT ANY POTENTIAL CONFLICT HAD PASSED BY THE TIME THE RA HAD OCCURRED; AND THAT HE HAD CONSIDERED THE SAFER AVENUE WAS TO CONTINUE COMPLYING WITH OUR ALT CLRNC SINCE THERE WAS NO POSSIBILITY OF GETTING ANY CLOSER TO THE TARGET AT THAT TIME. AT THE TIME; I WAS OF THE OPINION THAT REGARDLESS OF THE APPEARANCE OF A FALSE WARNING; IT WOULD HAVE BEEN SAFER TO COMPLY WITH THE RA KNOWING THAT IT WOULD BE A BRIEF DEV AND THERE MIGHT HAVE BEEN SOMETHING ELSE THAT TCASII WAS RESPONDING TO THAT WE WERE UNAWARE OF. IN ANY EVENT; I CALLED TPA APCH CTL AFTER GATE ARR. I TALKED TO THE SUPVR AND WAS TOLD THAT THE TARGET WAS A KING AIR AT 10000 FT. HE CONFIRMED THAT WE HAD BEEN CLRED TO 10000 FT AND IFR SEPARATION HAD NOT BEEN COMPROMISED. HE ALSO ACKNOWLEDGED THAT THE CTLR HAD BEEN VERY BUSY. I GUESS THE CTLR REALIZED THAT THE TURN HE HAD ASSIGNED WAS GOING TO BE SUFFICIENT TO KEEP LEGAL SEPARATION; BUT THE CLOSENESS OF THE ENCOUNTER GAVE US SOME ANXIOUS MOMENTS AND COULD HAVE VERY EASILY RESULTED IN US HAVING TO VIOLATE OUR ALT CLRNC TO COMPLY WITH TCASII. IN HINDSIGHT; I WISH THAT IN ADDITION TO THE TURN; THE CTLR WOULD HAVE TOLD US TO CLB BACK TO 11000 FT. ONCE WE HAD REACHED 11000 FT THERE WOULD HAVE BEEN NO POSSIBLE CONFLICT.