B767 Captain reported uncommanded aircraft movement during push back when miscommunication occurred with ground personnel. The Captain immediately stopped the aircraft; with no injuries or damage reported.

Narrative

Started right engine in the blocks due to inop APU. Pushback started out ok; a little slow and several significant left/right corrections. We were stopped about 10 feet right of centerline at an angle with no wing walkers; and the push crew said something very non standard and unintelligible. I asked him to say that again; to which there was no reply. Approximately 15 seconds later; we began to roll forward. I thought we were still connected to the tug and he was putting us on centerline. I heard him yell; 'set brake set brake'. I immediately stopped the aircraft. We may have rolled 1 or 2 feet. I asked if everyone was OK. He said yes. I asked if we hit anything; he say no. I asked him to put us on centerline and facing forward. He got us there after a few more minutes. I asked him once again to verify we didn't hit anyone or anything during this apparent unannounced disconnect. He verified once again the aircraft didn't hit anything and no one was injured. He apologized and we taxied for takeoff. Insufficient training. Put safety first.