There are SOPS covering this procedure but I have noticed the deterioration in adherence by some ground crews. This I put down to the ever increasing pressure put on handling companies for quick turnrounds. There is no doubt in my mind the pushback is directed by the flight deck. Unfortunately some crews think it works the other way. Pushback I had a while back went a bit like this.
Me: "Flight deck to ground good evening"
GND: "Flight deck release brakes"
Me: "flt deck/gnd negative, can I have your checks please"
GND: "complete, please release brakes"
Me: "flt deck/gnd again negative, we will get pushback clearance standby"
Once we had got clearance and I had released brakes I swear they started pushing instantaneously. The shame of it is that SOPS are followed not only to protect the aircraft, but more importantly to safeguard the ground crew.