CLRNC GIVEN DURING LNDG ROLL AND ENG REVERSING CAUSES CONFUSION. A RWY INCURSION RESULTS FOLLOWED BY A GAR OF ARRIVING TFC.

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AFTER TOUCHING DOWN FOR LNDG ON RWY 1 (AT DCA WASHINGTON NATL ARPT) FOLLOWING THE MOUNT VERNON VISUAL APCH THE TWR GAVE A HURRIED AND UNEXPECTED COMMAND TO OUR FLT; TO 'TURN AT THE NEXT INTXN.' I WAS FLYING AND CTLING THE ACFT AND QUICKLY TURNED OFF RWY 1 AT THE NEXT INTXN; WHICH HAPPENED TO BE RWY 33. NEXT THE TWR CTLR GAVE ANOTHER INSTRUCTION TO 'TURN OFF RWY 33' AS SOON AS POSSIBLE. AGAIN I IMMEDIATELY TURNED OFF AT THE NEXT TXWY; WITH CAUTION DUE TO THE AIRPLANE IN FRONT OF ME. NEXT THE TWR GAVE INSTRUCTIONS TO CALL HIM. AFTER SECURING THE ACFT I CALLED THE TWR TO DISCUSS THE INTENTION OF HIS INSTRUCTIONS. HE SAID HE HAD TOLD US TO 'CROSS RWY 33 AND THEN TO TURN AT THE NEXT INTXN.' NEITHER DID I NOR ANY OF MY OTHER 2 CREW MEMBERS HEAR THE FIRST PART OF HIS XMISSION 'TO CROSS RWY 33.' OUR TURNING ONTO RWY 33 CAUSED THE TWR TO HAVE THE PLANE LNDG ON RWY 33 TO GO AROUND. I MIGHT ADD THAT AT NO TIME WERE WE ADVISED THAT ANOTHER ACFT WAS LNDG ON RWY 33. ALSO; I BELIEVE WE SHOULD HAVE BEEN GIVEN THE INSTRUCTION TO TAXI THROUGH RWY 33 WELL BEFORE THE TIME WE RECEIVED THE CLRNC; WHICH WAS AT A HIGH WORKLOAD TIME WITH HIGH NOISE LEVEL FROM ENG REVERSING AND BRAKING. THE ATIS DID SAY MULTIPLE RWYS WERE IN USE.