YES, my experience is that there are differences in execution based on WHO pushes the turn counter button. I agree that this is undesirable for Map and Module level buttons, unless specifically intended by the designer.
SO, IMHO, it is good to have the ownership of the button activation cascade through the system so that the designer MAY use this to filter / change effects based on triggering player-side if desired.
BUT, it is undesirable that the system makes it impossible to override the masking of traits for buttons at the Map and Module level.
HOWEVER, there is some mitigation in place in that the designer can control, to some extent, which traits are exposed “below” the masking trait. In many cases this will allow the desired functionality. AND, it could be argued that this is a reasonable way to keep it. But, again, my preference would be to ignore triggering player-side for Map and Module level buttons while maintaining the cascade of the property for use by the designer in Beanshell statements if such differentiation is desired.
You are talking about deep, fundamental Vassal mechanics. If you have unit-level behaviour that you want to be executed by any player, including non-owning players of masked units, then don’t hide it behind restricted traits or the Mask. Otherwise cheating becomes trivial, just add a map level button to your copy of the module to flip everyone elses masked units.