Air Carrier First Officer reported a late instruction from ramp control; a miscommunication with the push back crew and a momentary loss of control of the aircraft during push back from the gate.

Narrative

I was FO (First Officer) for this flight; and we were to depart out of Gate XX from ZZZ. The crew accomplished our pre-flight duties and closed out as usual. As FO I called Ramp Control for pushback and received instruction to pushback tail to the East abeam Gate XY. The CA (Captain) relayed this to our ramp crew; and we began our pushback. During the push; Ramp Control issued us new pushback instructions to now face our tail to the South. I readback the instructions and CA relayed this to our rampers. Normally I listen to the ground crew along with CA; however ramp frequency was congested; and I could tell that the Ramp Controller was becoming increasingly unsure of how to facilitate traffic in/out of our ramp; so I opted to focus Ramp Control and was not listening to the ground crew with CA. We completed our pushback and as our ground crew was disconnecting; Ramp Control called with further amended instructions to now pushback to Gate XY. CA signaled to the ground crew; re-established communications with them and relayed our amended push instructions. CA asked if ground crew were connected and ready for the brake to be released and I heard CA confirm ground crew's apparent control of the aircraft and that they were ready for the brake to be released and he then said he was releasing the brake (note I was not listening to the ground crew so I could only hear CA's communication to them). After CA released the brake; the aircraft began to slowly roll backwards and both of us recognized this as uncontrolled aircraft movement and that the ground crew tug was not connected to the aircraft. CA took swift corrective action by setting the parking brake; and aircraft movement stopped. I heard CA query the ground crew about the status of their connection to the aircraft and requested better communication from the ground crew as to their status of aircraft control. CA made a PA to the passengers stating the reason for the sudden stop and that everything was now under control. The ground crew re-connected to the aircraft; resumed pushback; and the flight continued safely to our destination without incident.It was apparent that Ramp Control was struggling to facilitate aircraft movement in and out of the ramp with arriving aircraft awaiting our push to continue to their gates. This resulted in multiple amendments to our pushback instructions; the last of which came as ground crew had already disconnected from the aircraft. This could have confused our ground crew and lead to their apparent miscommunication to CA regarding the status of their connection to the aircraft and readiness for our brake to be released.When possible; avoiding situations where pushback tugs need to be disconnected and then reconnected could prevent ground crew confusion as occurred with our flight. Also as an FO; staying aware of what is occurring during the pushback; even if having to frequently communicate with a saturated Ramp Control during the push; is essential in the potential event that the CA does not notice uncontrolled aircraft movement so that you can step in and take corrective action if needed.