There is no “standard” for implementing a buddy box system so each maufatcerer may implement differently. When you use a buddy box on two Futaba radios, the settings (e.g. trims, servo reversing, dual rates) switch to whatever radio is active. This allows the instructor to have full throws, while the student can be on the dual-rate for example.

I don’t know about JR, but I would look at the expo and DR settings on the student radio. If they are set differently on the student’s radio than the instructor’s, that might be the place to start.