RPTR UNJUSTLY FAULTS HIS TCASII RA DURING AN ALTDEV ALT OVERSHOT BY MLT ON DEP PROC.

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INBOUND FROM BRDGE INTXN TO KTPA TALKING TO TPA APCH WITH CLRNC RNAV DIRECT KTPA; CROSS MACDILL AT OR ABOVE 2600 FT. APCH SAID 'I HAVE A 141 OFF MACDILL WITH CLRNC TO 1600 FT BUT I'M NOT TALKING TO HIM. WE WERE DSNDING TO 2600 FT; SAW THE 141. AS WE APCHED 2600 FT TCASII WENT OFF WITH A 'DSND XING DSND.' ALL THE REST HAPPENED IN ABOUT 15 SECONDS. MUCH FASTER THAN YOU CAN READ ABOUT IT. I STARTED TO FOLLOW THE TCASII RESOLUTION UNTIL I WAS SURE THE RA WAS ON THE 141 (WHICH IT WAS). I DSNDED ABOUT 100 FT BELOW THE 2600 FT ASSIGNED BEFORE I WAS SURE THE 141 WAS THE RA TARGET I ALSO TURNED L BEHIND THE 141 WHICH HAD CLBED ABOUT TO 2200 FT AND TURNED SLIGHTLY IN TOWARDS MY ACFT. IT WAS CLR THE 141 HAD BROKEN HER ALT BUT SHE SUDDENLY PUSHED OVER AND STOPPED HER TURN. MY IGNORED XING DSND RA BECAME A 'CLB; CLB; NOW' RA WHICH DISTRACTED ME FURTHER; THOUGH THE 141 WAS GETTING 95 PERCENT OF MY ATTN AT THIS POINT. ONCE IT WAS CLR THAT WE WERE DECONFLICTED; THE 141 APOLOGIZED TO APCH FOR BREAKING ALT. IF THE 141 WAS FOLLOWING AN RA AS I ALMOST DID; I UNDERSTAND HOW HE GOT OFF ALT. TPA APCH SAID SOMETHING TO THE 141 ABOUT HIS ALT; BUT IF THE 141 WAS TCASII EQUIPPED AND FOLLOWING AN RA HE SHOULD NOT BE VIOLATED. HAD I FURTHER FOLLOWED MY FIRST RA I WOULD HAVE CROSSED WELL INTO MACDILL'S CLASS C AIRSPACE AND CAN WELL UNDERSTAND THE 141'S FLT PATH. OTHER THAN THE TCASII GOING OFF I NEVER FELT THREATENED THROUGH THE ENTIRE EVENT. AS A RETIRED NAVAL AVIATOR I HAVE SOME FAMILIARITY WITH ACFT IN MUCH CLOSER PROX THAN THIS SIT. I AM ALSO SENDING COPIES OF THIS RPT TO MACDILL OPS IN HOPES THEY CAN GET IT TO THE 141 CREW IF THEY NEED IT AND TPA APCH SO THEY CAN GET A DIFFERENT PERSPECTIVE ON THE 'EVENT.' THIS IS THE FIRST AND ONLY TIME TCASII WAS NOT A BIG HELP WITH AIR TFC. IN IMC THIS COULD HAVE BEEN UGLY BECAUSE I WOULD HAVE FOLLOWED MY FIRST RA.