Air carrier Captain reported; at a foreign station; due to non standard push back hand signals the aircraft had been released and begun to roll back.

Narrative

During pushback; the Crew Chief signaled a non-functioning headset after the jetbridge disconnected. When a signal by the PF (Pilot Flying) depicted the park brake was released in preparation for pushback; the PM started to call for pushback. Without any signal to the ground crew; they commenced a pushback without a visual cue or clearance from the flight deck Fortunately; the out-station was not busy and no conflict with ground traffic existed. During pushback; only the left wing walker remained visible until nearing a possible termination of the pushback. With an unknown signal that lacked clarity from the ground crew to the flight deck (one arm vertical; the other pointing at the nose of the aircraft) the PF did not set the park brake thinking we were going to get pulled forward by the tug. Again lacking a clear signal from the ground; the flight deck signaled a start for the #1 engine and received a clearance to start. The ground crew person then returned to the signal previously mentioned (unclear and non-standard). The PF attempted to get a thumbs up confirmation to set the park brake but the tow guide kept the non-standard signal. The PF even opened the flight deck window to confirm the brake set signal and to clarify the unknown signal from then ground crew. The signal never changed and there was uncertainty if she was pointing at the engine; the aircraft nose; tow bar or nose gear light depicting the park brake set. It was at this time; unknown to the flight deck; that the push crew disconnected from the aircraft; without confirmation of brake set or clearance to do so. Simultaneously; the PM witnessed a ground time member run to the right side of the aircraft while the PF detected aircraft movement due to the idle thrust of an engine start. Only after a brief movement did the tug driver become visible and give the proper signal to set the brakes. The aircraft moved uncommanded; without positive control for 1-2 feet. The rest of the engine start and taxi out was uneventful. Three of the four ground crew were witness discussing the event as the tug driver returned to the gate. It is undetermined if the ground crew person giving the incorrect signal and procedure was wearing a specific safety vest that typically denotes a trainee.Cause: Inability to pre-brief loss of comm procedures with a ground crew following the retraction of the jet bridge. Additionally; the possibility of a language barrier at a foreign outstation may exist. The pressure to get the out" time at any outstation causes a deliberate stressor to take shortcuts. Lastly; the use of non-standard; vague signals for a procedure that requires them to be standardized in the interest of safety was the biggest factor. Solution: Additional training on standard ground crew signals to flight crew regarding brake release; pushback; engine start; brake set or emergencies."