Air carrier Captain reported the tug driver began moving the aircraft at the gate without coordinating with the flight crew. Captain directed the driver to stop; then the driver pushed the aircraft a second time without coordinating with flight crew.

Narrative

ZZZZ operations are not standard. First; Operations Rep/ Gate Agent did not advise the captain of boarded FAMS (Federal Air Marshal). Thankfully; the Purser did. I asked the Gate Agent at predeparture why I wasn't advised by their team and did not receive a sufficient explanation. Secondly; and more concerningly; after establishing intercom contact with the tug driver and giving the 'brakes released; standby' verbal instruction; the tug driver began uncommanded movement of the aircraft. When immediately queried and told to stop movement; his response was that he needed to release the chocks. I strongly advised that there is no aircraft movement without coordination with the flight deck. He apologized. We were then holding position at the gate with ground control telling us they would 'get back to us' shortly due to a controlled takeoff time when; most alarmingly after the previous discussion; the tug driver suddenly began to push the aircraft; again WITHOUT advising or asking the captain prior to commencing movement. When I commanded him to stop the pushback; he quickly complied. Had his response been slightly delayed; I was prepared to brake the aircraft from the uncommanded movement thinking we had experienced a 'breakaway' incident which could have caused mechanical damage to the tires and gear struts while being actively pushed by the tug. The tug driver's response to why he began pushing the jet without verbal clearance was that the Follow Me guide vehicle was giving him guidance to push. He was again advised to hold position and standby as the ground controller did not yet give us verbal clearance via radio. I reiterated that he needed to verbally coordinate ANY movement of the aircraft with me prior to the action. We then queried ground control and were finally given verbal clearance and directions to push and follow the Follow Me/ guide vehicle. The Disconnect SOP was also non-standard with push crew simply stating; 'Aircraft Disconnected' versus Aircraft disconnected; by-pass pin removed."I had to advise them to pull the nosewheel safety bypass pin as we still had the 'nws steering locked out' message displayed. Several issues from LEO (Law Enforcement Officer)/FAM notifications to significant aircraft movement safety issues are presented that need repair by ground crew reviewing and following SOP. Lastly; the coordination between ground control and the Follow Me guide vehicle is in question. Is it safe to assume that the guide vehicle is a physical extension of Ground Control's non-radioed (to aircraft) instructions? If that is the local airport convention; then the 10-1 pages need to include the information that guide vehicles instructions equate to ATC ground clearance for aircraft movement and the 10-1 pages need to be revised versus how they currently read (see attached photos). Regardless; the tug driver really needs an SOP review before personnel are hurt or equipment is damaged."