A319 ACFT ROLLS AFTER TOWBAR DISCONNECT. BRAKES WERE NOT SET.

Narrative

WE PUSHED BACK AT PHL. THE PUSHBACK SEEMED SLOWER THAN NORMAL AND I HAD TO TELL THE GUY TO HOLD POS IN THE BEGINNING AS HE WAS GOING TO PUSH BEFORE WE GOT CLRNC. THE FO AND I DISCUSSED IF THIS WAS DRIVER'S TRAINING GOING ON. WE WERE NOT NOTIFIED OF ANY TRAINING. AFTER WE STOPPED; THE TUG DRIVER DIDN'T SAY ANYTHING AND WE WONDERED IF HE WAS GOING TO PULL US FORWARD. THE NEXT THING I KNEW; THE TUG DRIVER SAID THE TOWBAR WAS DISCONNECTED! AS A PAVLOVIAN RESPONSE; I CLRED HIM TO DISCONNECT AT THE SAME TIME MY BRAIN REGISTERED: 1) HE HADN'T TOLD US TO SET THE BRAKES; AND 2) MY PERIPHERAL VISION NOTICED MOVEMENT. I IMMEDIATELY STOPPED THE ACFT. THERE WAS NO VIOLENT STOP AS I CAUGHT IT VERY FAST. THIS COULD HAVE BEEN A HORRIBLE ACCIDENT INJURING PERSONNEL OR DAMAGING EQUIP. WE WERE SAVED BECAUSE I HAD ALL MY ATTN ON HIM AND NONE ON THE ENG START. PER SOP THE CAPT IS RESPONSIBLE FOR MONITORING ENG PARAMETERS WITH THE FO DURING START; BUT I PAID MORE ATTN TO HIM BECAUSE HE DIDN'T RESPOND QUITE RIGHT WHEN THIS PUSHBACK STARTED. I WOULD LIKE TO SUGGEST THAT IT BE MANDATORY TO TELL THE CREW IF TUG DRIVER OR WING WALKER TRAINING IS GOING ON AND THAT THE TRAINER BE ON THE INTERCOM ALSO. THAT WAY HE WOULD HAVE KNOWN THAT HIS TRAINEE HAD NOT TOLD US TO SET THE BRAKES.