FLT CREW OF DC10-30 THREATENED WITH VIOLATION BY TRACON WHEN ALLEGEDLY COMPLYING WITH TCASII RA RESULTS IN CLB ABOVE CLRED ALT.

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OUR FLT TOOK OFF FROM RWY 18L AT ZZZ. CLRNC WAS TO FLY HDG 180 DEGS AND CLB TO 5000 FT. NEXT ATC CLRNC WAS TO TURN R TO A HDG OF 270 DEGS AND CLB TO 7000 FT MSL. AUTOPLT WAS ENGAGED APCHING 6000 FT. WE WERE CLBING AT APPROX 4000 FPM PRIOR TO AUTOPLT ENGAGEMENT. AT ABOUT 6000 FT WE RECEIVED A TCASII TFC ALERT. ZZZ DEP CTL ADVISED OF TFC AT OUR 10-11 O'CLOCK POS. WE SAW TFC VISUALLY AT OUR 11 O'CLOCK POS AND WERE TOLD IT WAS AT 8000 FT MSL. AT APPROX 6300 FT MSL WE RECEIVED A TCASII RA WHICH SHOWED A GREEN BAND CLB UP TO 1500 FPM WITH RED BAND ABOVE 1500 FPM. AUTOPLT WAS DISCONNECTED AND CLB WAS ADJUSTED TO LESS THAN 1500 FPM TO FOLLOW THE RA. THE RA WAS FOLLOWED UNTIL APPROX 7100 FT MSL WHEN THE TCASII ANNOUNCED; 'CLR OF CONFLICT.' NOT BEING SURE THAT THE TFC IN SIGHT WAS THE CAUSE OF OUR TCASII RA; I CONTINUED TO FOLLOW THE TCASII RA PAST 7000 FT MSL TO APPROX 7100 FT MSL WHERE THE TCASII ANNOUNCED 'CLR OF CONFLICT.' WE TOPPED OUT OUR CLB AT 7200 FT MSL AND THEN RETURNED TO 7000 FT. ATC SAID TO MAINTAIN 7000 FT. WE INFORMED ATC THAT WE HAD A TCASII RA. NO MORE WAS SAID UNTIL DSNDING INTO AUS WITH ZFW. WE WERE TOLD TO CALL ZZZ TRACON AND THEY GAVE US A PHONE NUMBER. AFTER LNDG; I CALLED AND WAS TOLD THEY WERE GOING TO FILE A PLTDEV RPT. AS A CONTRIBUTING FACTOR: I WOULD HAVE TO QUESTION THE 270 DEG HDG AND CLB TO 7000 FT CLRNC THAT RESULTED IN THE TCASII RA. I BELIEVE THE CREW FOLLOWED CORRECT PROC IN RESPONDING TO A TCASII RA. SUPPLEMENTAL INFO FROM ACN 634673: WE WERE NOT TOLD OF ANY TFC PRIOR TO OUR 270 DEG HDG VECTOR.