EMB 175 Captain reported the push back tug driver failed to connect the tug properly; the aircraft was moving back unattached; and the Captain quickly applied brakes.

Narrative

Gate was XX. We were ready to push back; and all checklists were complete. They didn't have a tug/tron available at the time; so we were running about 10 minutes behind schedule. Once the ramp got one and hooked it up; we followed the standard SOP call to flight deck to ramp to make sure everything was ready to go. I noticed too while they were bringing the tron over it was more the style of where it picks you up without the straps; so I knew to suspect hardly any movement once the brake was released. Once the parking brake was released; we started rolling backwards at an alarming rate. I reached up to turn the HYD SYS 1 and 2 to on to get the brakes to work without having to use the parking brake lever. During all this time the ramper had said nothing. Once I reset the parking brake I had asked him if everything was done right since we moved so much. He didn't have much of any response other than 'I forgot the switch'. At that time; I had asked for Operations to watch the footage since they had a camera on us and confirmed that it was moving freely and not connected. I asked for a different tug driver just to have a fresh mind pushing us back and not thinking of what just happened. The ramp manager came over and asked what happened. I had explained everything I could. I'm not sure he understood what had happened because he didn't seem to care too much. I had sent a a message to the station manager. After about 15-20 minutes we had a new tug driver and was able to push back in ZZZ.Cause: I can think of the ramper being told by a higher up at the station just go get an out time and we'll get the rest. Being rushed/being behind. Suggestions: Don't stress being late. I understand the whole short staffed/not having enough equipment to do the job can cause a lot on just try to get an out time since we were already delayed. Being better trained on the equipment you use.