C182 PLT CHALLENGED BY DVT GND CTLR FOR NOT FOLLOWING LCL CTLR INSTRUCTIONS.

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ON LNDG ROLLOUT ON DVT RWY 25L; I BEGAN TO EXIT THE RWY AT TXWY A1 HIGH SPD INTXN. DURING THIS TIME; THE LCL CTLR ADVISED ME TO 'TURN L ONTO TXWY C AND CONTACT GND.' TXWY C IS THE PARALLEL TXWY TO RWY 7R/25L. I EXITED THE RWY AT TXWY C6; AND TURNED L ONTO TXWY C EBOUND. I THEN SWITCHED TO GND FREQ AND WAS PREPARING TO ADVISE THEM THAT I WAS UP ON FREQ AND PROCEEDING EBOUND TO PARKING. BEFORE I COULD DO THIS; GND CALLED UP ASKING WHO I WAS AND WHAT I WAS DOING ON THE TXWY. I REPLIED THAT LCL HAD TOLD ME TO TURN 'ONTO' TXWY C AND CONTACT GND; AND I WAS DOING JUST THAT. GND REPLIED THAT I WAS WRONG; THAT MY CLRNC WAS TO TURN OFF THE RWY ONTO THE HIGH SPD TXWY; HOLD SHORT OF THE PARALLEL TXWY; AND CONTACT GND FOR TAXI CLRNC. ATC PHRASEOLOGY: AT THE TIME; THERE WERE MAYBE 3-5 ACFT IN THE PATTERN; WITH ONLY MYSELF ON THE GND. WHEN THE TFC COUNT IS LIGHT AS IT WAS; LCL WILL SOMETIMES JUST HAVE YOU EXIT THE RWY AND MONITOR OR CONTACT GND WHILE TAXIING TO PARKING. TO ME; 'TURN L ONTO TXWY C' MEANS TO TURN ONTO THE PARALLEL TXWY C. HAD THE CLRNC FROM LCL BEEN 'ACFT XXX; TURN L NEXT EXIT; TXWY C6; ETC; CONTACT GND;' THEN THAT MEANS TO ME; EXIT THE RWY ON THE HIGH SPD TXWY; CLR THE RWY; BUT HOLD SHORT OF THE PARALLEL TXWY; AND CONTACT GND FOR FURTHER CLRNC. I BELIEVE I FOLLOWED THE CLRNC I WAS GIVEN. THE GND CTLR FURTHER STATED THAT HAD THERE BEEN AN ACFT ON TXWY C; THERE COULD HAVE BEEN A GND COLLISION. I DID VISUALLY CLR AFTER EXITING THE TXWY. I BELIEVE THAT ATC SHOULD CHK THEIR PHRASEOLOGY; AND BE MORE SPECIFIC WHEN NECESSARY.