FLC IN A C550 ON STAR ARR WERE QUESTIONED BY ARTCC CTLR IF THEY WERE IN A L TURN FOR A HDG CHANGE AT THE STAR FIX JUST PAST.

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I WAS THE PNF; FO; WHEN WE WERE INBOUND TO AFW ON THE DODJE 3 ARR. THE FMS WAS SET UP FOR THE STAR AND THE AUTOPLT WAS FLYING. WE HAD COMPLETED THE APCH CHKS AND I WAS LOOKING AT THE APCH PLATE. I DID NOT NOTICE THAT WE HAD PASSED CABBY INTXN WHERE WE WERE SUPPOSED TO TURN TO A 280 DEG HDG. THE ATC CTLR ASKED US IF WE WERE IN THE L TURN. ALTHOUGH THE CAPT LOOKED AT THE ARR HE AS UNAWARE THAT A TURN TO 280 DEGS WAS REQUIRED. SINCE I WAS LOOKING AT THE APCH PLATE I DID NOT NOTICE THAT HE DID NOT TURN. SINCE THE FMS AND AUTOPLT WERE FLYING; IT CONTINUED TOWARDS ITS NEXT FIX (AFW) AND DID NOT TURN. PLTS REALLY NEED TO PAY ATTN AND NOT ALWAYS DEPEND ON THE FMS BECAUSE IT DOES NOT ALWAYS DO THE RIGHT THING. THIS SIT IS A PERFECT EXAMPLE OF THAT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT HE AND THE CAPT DID NOT THINK THAT THE STAR INDICATED THAT THEY WERE TO TURN L TO A 280 DEG HDG WITHOUT ATC'S INSTRUCTIONS TO DO SO. THEREFORE; THEY BELIEVED THAT THE CTLR WAS JUST TRYING TO FIND OUT IF A PREVIOUS CTLR HAD GIVEN THE HDG OR ANOTHER VECTOR INSTRUCTION.