The rudder trim switch works through the ACE and PFCs to move the trim actuator. The actuator is an electric motor located under the cockpit floor and moves the rudder pedals through mechanical linkages. Trim is accomplished by this movement, which, just like manual rudder inputs, move the rudder pedal transducers, which in turn command the rudder PCUs through the ACE and PFC units.
The trim cancel switch sends its signal to both ACEs and PFCs which return the trim to center unless the asymmetric thrust input is active. The PFCs communicate with the AIMS cabinets, which in turn send signals to the trim indicator on the center pedestal.
Your observance of the trim indicator behavior on reset is due to the fact that the trim indicator position is based upon the trim actuator movement (via pedal linkages) and not the actual rudder position.
Rudder operation is electro-hydraulic. Electric signals control solenoids and valves in the rudder PCUs, which in turn route hydraulic pilot pressure to control valves that move the rudders. The rudder tab is linked directly to the lower rudder, and moves according to rudder position.