Yes it has to do with play between the gears.
Also some gens have these kind of problems. For instance the minute hand of my gen Franck Muller, jumps forward a little when I push the crown back in.
Regarding the play you can try the following:
When you set the time, just set the minute hand a little too far and then turn it back to the right time.
so if it's 15 past, set it at 18 past and turn it back to 15 past.
The problem should be gone.