FLC OF AN LGT ACR ACFT INADVERTENTLY TURNED OFF RWY TOO SOON AFTER LNDG ONTO A NEW TXWY RESULTING IN A RWY EXCURSION.

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WHILE ON FINAL APCH IN NIGHT VFR CONDITIONS; I WAS THE FO FLYING THE ACFT; FLT ACR X DCA-ORD. WE WERE LNDG RWY 4R AT ORD AND ON FINAL WE WERE INSTRUCTED TO ROLL TO THE END; WHICH IS STANDARD FOR RWY 4R ARRS AT ORD. THE LNDG WAS UNEVENTFUL. HOWEVER; AS I WAS TRANSITIONING CTL OF THE ACFT TO THE CAPT; THE ORD TWR CTLR; IN RAPID CADENCE; INFORMED US TO TURN OFF AND CONTACT GND 121.9. I WAS NEVER CLR IF HE SAID 'EXPEDITE' OR 'NEXT TURN' OR 'ROLL TO THE END' BUT DUE TO THE NIGHT CONDITIONS AND MY PERCEIVED SENSE OF URGENCY; I APPLIED SLIGHT L RUDDER PRESSURE IN ANTICIPATION OF OUR L TURNOFF; AND THEN RELINQUISHED CTL OF THE ACFT TO THE CAPT. I PERSONALLY WAS UNSURE OF OUR EXACT LOCATION RELATIVE TO THE END OF THE RWY AND THE SUBSEQUENT TURNOFF. HOWEVER; AS THE CAPT TURNED OFF I THINK WE BOTH REALIZED WE HAD MADE AN EARLY TURNOFF. THE CAPT STOPPED THE ACFT ON THE TXWY CLR OF RWY 4R. TWR THEN TOLD US WE WERE NOT SUPPOSED TO TURN OFF THERE; BUT TO GO AHEAD AND TAXI STRAIGHT AHEAD AND CONTACT GND POINT 9. THERE WAS NEVER ANY CONFLICT WITH OTHER TFC AND NO MORE WAS SAID. IT TURNS OUT THAT WE EXITED ON A NEW TXWY (S5) THAT WAS CONSTRUCTED AS A RESULT OF THE NEW RWY 27L HOLDING/DEICING PAD WITHIN THE LAST YR. ON MY NEXT TRIP (3 DAYS LATER) THE PAPERWORK INCLUDED A MESSAGE TO BE AWARE OF AN EARLY TURNOFF ON THE SAME TXWY (S5) WE TURNED OFF ON; AND THAT SUCH A MOVE IS CONSIDERED TO BE A RWY EXCURSION OF RWY 9R/27L. I BELIEVE THAT NIGHT VISIBILITY; INADEQUATE RWY LIGHTING; AND THE TWR CTLR'S 'HUSTLE UP' VERBIAGE DURING WHAT IS ALWAYS A CRITICAL PHASE OF FLT WHILE WE WERE STILL ON THE RWY CONTRIBUTED TO OUR SUBSEQUENT ERROR.