AN MLG AND A WDB HAD AN LTSS THAT APPARENTLY WAS CAUSED BY PLT ERROR IN NOT STARTING TURN IN A TIMELY MANNER.

Narrative

ATC GAVE US A L TURN TO 360 DEG (APPROX 65 DEG L TURN) AND DSND TO FL290. (DSCNT WAS GIVEN FIRST; FOLLOWED BY THE TURN). WE WERE DSNDING AT APPROX 1100 FPM AND TURNING TO 360 DEG WHEN TCASII ACTIVATED AND SHOWED A RED ARC EVERYWHERE EXCEPT 1500-1800 DOWN. I TOOK ACFT FROM FO AND STEEPENED TO ABOUT 1800 FPM (SOMEWHERE IN GREEN ARC). WE SPOTTED A WDB PASSING DIRECTLY OVERHEAD ABOUT 500 FT HIGHER. WE COMPLETED TURN AND LEVELED AT FL290. TCASII GAVE US A CLR OF TFC AS WDB PASSED OVERHEAD. ATC THEN ASSIGNED A R TURN TO 090 DEG AND REINTERCEPTED J-42; AS FILED. I WAS SURPRISED TO GET A RA FROM THE TCASII (FO AND I BOTH COMMENTED ON THE SUDDEN L TURN AND DSCNT). I PERHAPS WAITED 1-2 SECONDS LONGER BEFORE PUSHING OVER TO ACHIEVE A FASTER DSCNT RATE. SUPPLEMENTAL INFO FROM ACN 220937. WHILE CRUISING AT FL330 SW OF BNA VOR ON J-42 NEBOUND; ZME GAVE US A TURN TO 360 DEG FROM A BASE HDG OF 071 DEG. WITH SUCH A LARGE HDG CHANGE FOR NO APPARENT REASON; I SUSPECTED A TFC CONFLICT; BUT NONE WAS GIVEN BY ATC. IN ADDITION; OUR ACFT WAS TCASII EQUIPPED AND THERE WAS NO CONFLICT SHOWN. ATC THEN GAVE US AN IMMEDIATE DSCNT TO FL290 -- AGAIN NO MENTION OF CONFLICT. WHEN ATC ISSUES AN OFF-COURSE VECTOR WHILE IN THE CRUISE CONFIGN; THE NORMAL RESPONSE IS SLOW AND EASY (IE; KEEP THE PAXS COMFORTABLE). WHEN ATC ISSUES A TFC CONFLICT; THE RESPONSE IS GENERALLY MORE IMMEDIATE. IN THIS SITUATION; I NEVER HEARD A TFC CONFLICT FROM ATC UNTIL I WAS ALREADY RESPONDING TO A TCASII RA. HAD ATC SAID SOMETHING ABOUT TFC AT FIRST; WE COULD EASILY HAVE PROVIDED MORE SEPARATION BTWN ACFT.