P50 CTLR QUESTIONS B737-300 FLT CREW'S NEED TO EXECUTE A TCASII CLB MANEUVER OVERFLYING ISSUED VFR TFC WHILE ON VECTOR FOR APCH TO PHX ARPT.

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ON ARR INTO PHX ON THE AIRLINE 3 ARR; WE WERE CLRED TO DSND FROM 11000 FT TO 10000 FT AND GIVEN TFC AT 11 O'CLOCK POS; A PIPER AT 9500 FT. WE DSNDED TO 10000 FT WHILE SEARCHING FOR TFC. THE TFC SHOWED UP ON THE TCASII AT 9700 FT AND WE WERE GIVEN A TCASII TA. UPON ARR AT 10000 FT; I SAW THE TFC AND THE CAPT RPTED TO ATC THAT THE TFC WAS IN SIGHT. SHORTLY AFTER CALLING THE TFC IN SIGHT; WE RECEIVED A TCASII RA 'CLB; CLB.' I DISENGAGED THE AUTOPLT AND BEGAN A CLB OF APPROX 200 FPM TO PUT THE IVSI NEEDLE IN THE GREEN ARC. THE CAPT RPTED TO ATC THAT WE WERE CLBING IN RESPONSE TO AN RA. THE CTLR RESPONDED BY ASKING WHY WE WERE CLBING AND STATING THAT THERE HAD BEEN NO LOSS OF SEPARATION. THE CAPT STATED THAT WE WERE CLBING IN RESPONSE TO AN RA. WE CLBED TO 10500 FT BEFORE RECEIVING THE 'CLR OF CONFLICT' ADVISORY AND RETURNING TO 10000 FT. THE CTLR AGAIN QUESTIONED WHY WE CLBED; SO I STATED THAT OUR REGS REQUIRE US TO COMPLY WITH A TCASII RA EVEN WHEN WE HAVE THE TFC IN SIGHT. THE CTLR CAME BACK SEVERAL MINS LATER AND ASKED US TO CALL TRACON ONCE ON THE GND. THE CAPT SPOKE WITH THE CTLR ONCE ON THE GND. SUPPLEMENTAL INFO FROM ACN 621963: WHEN I CALLED APCH CTL HE SAID THAT THE TFC WAS 500 FT BELOW US AND SINCE WE SAW IT THERE WAS NO NEED TO FOLLOW THE RA ALERT. I TOLD HIM THAT OUR TCASII INDICATED 300 FT. WE WERE ON A CONVERGENCE COURSE AND I WASN'T SURE IF THE OTHER ACFT WAS CLBING. HE SEEMED TO UNDERSTAND MY CASE AND THE CONVERSATION ENDED THERE.