CAPT RPTING HAD TCASII RA ON TFC THAT WAS SIGHTED AFTER DSCNT WAS COMMENCED. SECOND CAPT RPTING WAS THE TFC SIGHTED AND ALLEGES NEVER BELOW 29000.

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TCASII NOTIFICATION OF TFC CONFLICT. TCASII RPTED TFC INITIALLY AT 900 FT ABOVE AT 10-12 MI AT 12-1 O'CLOCK. TCASII DIRECTED US TO DSND AS THE TFC CONFLICT CONTINUED TO DSND. I FOLLOWED THE TCASII INSTRUCTIONS AND BEGAN MY DSCNT. I HAD DSNDED 200 FT BELOW ASSIGNED ALT WHEN ACFT WAS SPOTTED VISUALLY. THE DSCNT WAS STOPPED DUE TO NO CONFLICT AND WE CLBED BACK TO ASSIGNED ALT. CTLR WAS NOTIFIED OF ALT DEV AND WE ASKED THE CTLR ABOUT THE APPARENT CONFLICT. HE SAID HE SHOWED NO CONFLICT AND 1000 FT VERT SEPARATION BTWN ACFT. HE ALSO NEVER SHOWED US DEVIATING FROM ALT. I WAS LATER NOTIFIED TO CALL JAX CENTER BY TELEPHONE. I WAS ADVISED THAT THERE WAS NO PROBLEM. SUPPLEMENTAL INFO FROM ACN 189928: OUR FLT NBOUND AT FL290. WORKING CENTER OUR AUTOPLT LEVELED ACFT BY USING PMS (PERFORMANCE MGMNT SYS) AT 28960 CAP - 28940 FO SIDE APPROX. CENTER SHOWED US AT 290. ACFT SBOUND AT 280. I HAD ACFT VISUAL AT APPROX 12-15 MI. TCASII HAD A TRACK ALSO; INDICATING THAT ACFT AT 1 O'CLOCK; 900 BELOW AND LEVEL. AS ACFT APCHED WE RECEIVED A TA THEN AN RA 'MONITOR VERT SPD'. WE VISUALLY HAD ACFT DURING ENTIRE TIME THAT ACFT RECEIVED AN RA TO DSND. THEY NOTIFIED CENTER OF RA. THEY RPTED TO CENTER THEIR ACTION AND THEY SAID TO HAVE SPOTTED US VISUALLY AT THIS TIME AND STOPPED THEIR DSCNT. IT APPEARED THEY DSNDED APPROX 100-150 FT. OUR ALT NEVER CHANGED. CENTER SHOWED US BOTH AT 290 AND 280 RESPECTIVELY. I FEEL THAT THE TCASII FROM THE OTHER ACFT GAVE AN INCORRECT RA. NO ALT CHANGE WAS MADE TO CAUSE AN RA. I BELIEVE THE CREWS HAVE TO TRY TO VISUALLY CONTACT THE TARGETS TCASII TRACK TO BE ABLE TO USE THE 'OUTSIDE SCAN' IN SUPPORT OF TCASII.