Aztec Kid,
If you are referring to the sidestick priority button, whci I assume you are, then this may help. I realise that you are familiar with this but I offer for background.....
The sidesticks are obviously not mechanically interlinked, but the Flight Control processor combines the two stick inputs and adds them together algebraically. In the event that two opposing stick inputs are made simultaneously, then they effectively cancel each other out. The last sidestick button pressed is the stick that has priority. This is accomanied by an audio call out"Priority Left" etc. Should the inactivated stick be moved, then a Red Arrow is illuminated on the glareshield and the active side will get a green arrow indicating that the opposite sidestick is being moved.
In the event that the aircraft is being hand flown, and a tweak is required, then as you say, due diligence must be exercised with regard to increased control rates. Having spoken with other instructors relating to SOPs with different carriers, it seems that some actually disable the Glareshield lights to prevent junior pilots being distracted (or disappointed?) should the Training Captain/NHP intervene.
In my company, the use of the sidestick priority button is demonstrated initially in the ground school, and an example of possible usages give, including sometimes, Crew Incapacitation during hand flying
I hope that helps.
Tailwinds