CONFLICT BTWN AN ACFT JUST LANDED AND ACFT LNDG ON AN INTERSECTING RWY.

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AFTER A NORMAL APCH AND TOUCHDOWN ON RWY 36; WE WERE ROLLING OUT AND I UNDERSTOOD THE LCL CTLR TO INSTRUCT US TO TURN L (EXIT RWY) ON EITHER TXWY I OR RWY 33. (THE FO UNDERSTOOD THE TWR THIS WAY ALSO.) I DIDN'T QUITE HAVE THE AIRPLANE SLOW ENOUGH TO USE TXWY I; SO I PROCEEDED TO BEGIN A TURN ONTO RWY 33. AS I STARTED THE TURN; THE FO NOTICED AN LTT COMMUTER ON VERY SHORT FINAL TO RWY 33 WITH INSTRUCTIONS TO HOLD SHORT OF RWY 36. AS THE FO WAS ADVISING ME OF THE COMMUTER TFC; THE LCL CTLR TOLD US TO CROSS 33 AND EXIT RWY 36 AT TXWY J. I WAS ABOUT 45 DEGS INTO THE TURN ONTO RWY 33. I IMMEDIATELY TURNED R TO CONTINUE DOWN RWY 36 AND INCREASED PWR ON BOTH ENGS; WHICH WERE AT IDLE. WE WERE CLR OF RWY 33 BEFORE THE COMMUTER ARRIVED AT THE INTXN OF RWY 36 AND RWY 33. IT SEEMS IF THE CTLR HAD SAID 'EXIT AT TXWY I OR CROSS 33 AND EXIT AT TXWY J' BOTH OF US WOULD HAVE HEARD AND UNDERSTOOD IT. I DON'T THINK THAT IS WHAT WAS SAID. I WAS ALSO NOT AWARE OF THE RWY 33 TFC UNTIL THE FO SPOTTED HIM. PROBABLY WOULD BE GOOD IF CTLRS ALWAYS ADVISED YOU OF XING RWY TFC AHEAD OF TIME. IF THE COMMUTER HAD PROBS HOLDING SHORT; I MIGHT BE ABLE TO SAVE THE DAY IF I'M 'KEPT IN THE LOOP' AS TO WHAT IS GOING ON.