B737-800 flight crew observed nonstandard procedures by ground crew during pushback.

Narrative

I'm writing this with the sole intent to absolutely prevent aircraft damage and/or injury to someone in the future. We pushed off Gate XX at ZZZ with a Ramp Crew that was training the push back operator. I didn't know this by any briefing ahead of time (which would have been helpful by the more experienced Ramp Personnel instructing the tug operator) but instead only observed this on an incredibly slow push back; difficulty communicating standard callouts to her; and directly seeing in tight turns she was being instructed directly how to turn and when by the Instructor sitting next to her on the tug while we pushed to Spot XX. We were finally dropped off at an angle off the line of RH with our wing far left of centerline. I heard nothing about setting brakes when I finally hear her asking to 'disconnect headsets' and she's pulling the tug in reverse away from the aircraft and I do not have the brake set. Aircraft may have rolled slightly I stepped on the brakes slowly and stopped and said to her 'do you want me to set brakes?' She was totally confused and from what I gathered didn't even understand what just occurred as she responded with an attitude to disconnect. I told her to disconnect and set the parking brake and that was that. I fully understand that new people will make mistakes; that's ok. I get it. I was patient throughout the push kept all the calls totally standard and didn't bother her because I could see she was really new to this. I was patient. I'm just glad I caught the disconnect before we really started moving and no one got injured while disconnecting the tow bar or bypass pin. My main concern is this; that if this type of event goes unnoticed it could happen again with worse consequences.