FO OF AN A320 DISCONNECTED AUTOPLT IN RESPONSE TO A TCASII RA AFTER BEING TURNED OFF COURSE BY ARTCC CTLR FOR TFC SEPARATION.

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DEPARTED DEN REQUESTING FL370. CLRED TO FL290; ADVISED OF SEVERAL OTHER ACFT HDG FOR MSP AT FL330 AND FL370. LEVEL AT FL290 FOR ABOUT 5 MINS. CLRED TO FL330. 30-60 SECONDS LATER; CLRED TO TURN 40 DEGS L. NO 'EXPEDITE' OR 'TFC ALERT' OR URGENCY IN THE CTLR'S VOICE. NEXT XMISSION WAS TO ACR Y TO TURN 40 DEGS L. THIS GOT MY ATTN; BUT WOULD BE NORMAL IF WE WERE BOTH BEING SEQUENCED FOR MSP. A SHORT TIME LATER; WE GOT A TCASII TA. THE MAP RANGE NEEDS TO BE 40 MI OR LESS TO DISPLAY THE TFC. AFTER DOING THAT; THERE WAS A '+7' TARGET AHEAD AND TO THE R -- 4 MI(?). I THOUGHT THE TARGET WAS WHITE AT THAT TIME; BUT A REVIEW OF OUR MANUAL INDICATES IT SHOULD HAVE BEEN AMBER. IF IT WERE WHITE; MAYBE TCASII LOGIC WAS AFFECTED BECAUSE BOTH ACFT WERE ALREADY TURNING. SINCE THERE WAS NO RA YET; AND WE WERE STILL TRYING TO FIGURE OUT EXACTLY WHERE THE THREAT WAS; I PUSHED THE VERT SPD KNOB; WHICH CAUSES THE VERT SPD TO GO SMOOTHLY TOWARD ZERO (TURN CONTINUES). A FEW SECONDS AFTER THAT; WE GOT A DSND RA. I DISCONNECTED THE AUTOPLT AND BEGAN A DSCNT. ABOUT THAT TIME ACR Y ADVISED 'CLBING FOR TCASII RA' (PROBABLY WAS INITIALLY LEVEL AT FL310). AFTER THE RA; WE CONTINUED THE CLB TO FL330 AND EVENTUALLY WERE CLRED BACK ON COURSE. I'M SURPRISED THAT THE TCASII DIDN'T GIVE US A BETTER WARNING CONSIDERING OUR CLB RATE OF ONLY ABOUT 1000 FPM; EITHER AN EARLIER TFC CALL; OR AN INITIAL REDUCE CLB RA. MAYBE THE TURNS PUT US AT THE EDGE OF NOT NEEDING AN ADVISORY. THE A320 AUTOPLT TURNS AT A 15 DEG BANK ANGLE AT HIGH ALT CRUISE (NOT SELECTABLE AS ON SOME ACFT). IF THE CTLR HAD USED 'EXPEDITE' WITH THE INITIAL TURN; I COULD HAVE DISCONNECTED THE AUTOPLT AND USED A 30 DEG BANK ANGLE.