TUG DRIVER PUSHES B737 ONTO TXWY AFTER BEING TOLD TO HOLD SHORT OF THAT TXWY AT SAN.

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WE WERE AT GATE AT SAN. WE WERE SCHEDULED TO PUSH AT XA10. ALL THE PAPERWORK WAS DONE; AND CABIN DOOR WAS CLOSED. I CALLED FOR A PUSH CLRNC FROM SAN GND. AT THAT TIME I NOTICED A RAMP PERSON COMING WITH MORE BAGS; SO I TOLD GND THAT WE WOULD BE READY TO PUSH IN A FEW MINS. HE SAID THAT WE WERE CLR TO PUSH; KEEP CLR OF TXWY B; AND IF WE NEED TO GET ON TXWY B; CALL FOR AN ADDITIONAL CLRNC. I TOLD THE CAPT THAT WE WERE CLRED TO PUSH; MAINTAIN CLR OF TXWY B; AND IF WE NEED TO GET ON TXWY B I NEED TO CALL GND AHEAD OF TIME FOR THE CLRNC. THE CAPT SAID THAT WE WOULD NOT NEED THE ADDITIONAL CLRNC. I HEARD THE CAPT GIVE THE TUG DRIVER THE OK TO PUSH AND REMAIN CLR OF TXWY B AND THE TUG DRIVER REPEATED IT BACK: CLRED TO PUSH; REMAIN CLR OF TXWY B. AS WE WRE PUSHING BOTH THE CAPT AND I WERE BUSY MONITORING THE ENG START; AND DID NOT REALIZE THAT THE TUG DRIVER PUSHED THE ACFT ON TO TXWY B UNTIL GND CALLED AND TOLD US THAT WE WERE NOT CLRED ONTO TXWY B. THE CAPT TOLD THE TUG DRIVER TO STOP THE ACFT AND WHEN WE LOOKED AT WHERE WE WERE AT; SURE ENOUGH; WE WERE ON TXWY B. WE APOLOGIZED AND TOLD THE GND CTLR THAT WE GAVE THE TUG DRIVER THAT VERY INSTRUCTION AND ALSO THAT WE CALLED OUR OPS AND TOLD THEM TO TALK TO THE TUG DRIVER. THE ONLY POSSIBLE CONFLICT WAS WITH COMPANY ACFT EXITING ON THE HIGH SPD TXWY B5; BUT HE STILL HAD PLENTY OF ROOM. CONTRIBUTING FACTORS: ADDING LAST MIN BAGS; CAUSING DELAY IN PUSHING ACFT. THINGS THE CREW SHOULD HAVE DONE: DELAY THE ENG START UNTIL WE KNOW EXACTLY WHERE WE ARE BEING PUSHED. CALL GND FOR THE ADDITIONAL CLRNC.