Air carrier Captain reported a miscommunication with the ground crew and use of non-standard procedures when the aircraft rolled forward unexpectedly as ground personnel were disconnecting the tug.

Narrative

Cleared to push off of [the gate] in ZZZ. Push onto Taxiway 1; tail east. We commenced push and were cleared to start engine #2; which we did. We pushed onto Taxiway 1; as instructed and stopped. As we stopped; ZZZ Ground added that they wanted us to remain west of [taxiway 2]. We were right at [taxiway 2]. I told the Tug Driver they now wanted us west of [taxiway 2]. He was already in the process of starting to disconnecting us. I told him to hold on because we needed to stay west of [taxiway 2]. I did not set brakes because I believed we would have to move (and shut down the engine to move forward). I did not want to shut down the engine; so I prompted the F/O (First Officer) to negotiate with Ground; but before we did; the Ground Controller informed us our position was fine.At that point I could tell the Ground Crew was already under the aircraft. The problem of where to stop solved; and the Ground Crew already about to; or in the process of disconnecting; I said; 'Clear to disconnect'. They had never told me to set brakes. I had never said 'brakes set'. I had never set brakes. As they disconnected; the aircraft moved slightly; motion which both the Ground Crew and I noticed immediately. I set the brakes. They finished disconnecting and cleared the aircraft with no other issues.The last second instructions from Ground threw me off my rhythm. The Ramp never prompted me to set brakes. I said Cleared to disconnect" without brakes set. The Swiss Cheese all lined up; and not in a good way. I felt rushed to catch up to Ground and then Ramp. Rushing never helps."