A319 Captain reported the push bar became disconnected during pushback resulting in uncommanded aircraft movement. Captain applied brakes to stop aircraft.

Narrative

We were ready for pushback at gate X at ZZZ with all the checklists completed. I established intercom contact with the ground crew push tug driver asking him if the ground crew is ready; who replied that the ground crew is prepared for departure and that he wants me to release the parking brake. I acknowledged this and I released the parking brake and instructed the First Officer to call ramp control for the pushback clearance. As we were listening to ramp instructions the push back driver said 'Set parking brake' and few moments later First Officer noticed and said 'We are rolling back'. I immediately applied the brakes and set the parking brake. We did not hit anything.The push tug driver reported that the push bar was not connected properly and that it disconnected from the aircraft at start of pushback. I called Maintenance Control and made the maintenance report entry. A company mechanic came out and did a visual inspection and concluded that there was no damage done to the aircraft. A new maintenance report was sent through ACARS and we pushed back again without an incident.It is worth noting that the push tug driver did not use the proper terminology during the breakaway incident. He tried to vaguely say 'Set the parking brake' instead of properly announcing 'Breakaway; Breakaway!'. This call would immediately bring my attention to the fact the plane is no longer attached to the tug and is rolling back. It was the First Officer who noticed and immediately announced 'We're rolling back!'. Using incorrect terminology inhibits effective communication and could have potentially wasted valuable seconds as we were rolling back. It is important for the ground crew to properly use the training they receive and to use the proper terminology in order to avoid incidents such as this one.