OK - here's a stab.
So - with everything all hooked up, you can feel the added roll force in the whole system, although it is being generated only by the added servo torque connected to the LH flaperon.
NOW - you pull the flap handle to the first notch. Both push rods want to move in unison, but the LH rod has the added resistance generated by the roll servo and so the system becomes unbalanced. The RH rod moves more (a lot more) than the LH rod, the RH flaperon moves down and the stick moves to the left inducing a LH roll.
This is hands-off the stick. Try it. When you hold the stick - even very lightly - you both resist and inhibit this motion without noticing. John Stamper seems to have confirmed this theory in his comment.
Good observation Bob, but I don't think it has anything to do with what is being described.
The aerodynamic feedback force from the flaperons, while that airplane is in flight, is far higher than the friction from the autopilot roll control servo. So actions that you see happen with the airplane sitting in the hangar, will be totally different when there is aerodynamic forces on the system.
I have flown RV-12's with, and without autopilots that did not have this characteristic. I am sure it is a rigging or construction issue.
A few comments....
Flaperon shape can have an effect on roll trim. The effect can be significant
if there is a large shape difference between the left and the right.
The aft skin portion of the flaperons should be totally flat cord wise, from the skin lap joint, all the way aft to where the trailing edge radius starts, when checked with a straight edge.
I have corrected roll trim problems on many RV's in one try, just by reshaping the flaperons or ailerons while checking for correct shape with a straight edge.
Once you have confirmed that the flaperon shape is correct. You should confirm that the flaperon vertical position is correct (rod end adjustment).
After confirming that, you should confirm that the flaperon rigging is correct. Flaps retracted and stick in neutral position, each flaperon should be drooped down between 1/16" and 1/8" relative to the wing tip (this is because with a slight amount of elasticity that exists in the control system, the flaperons deflect up about that amount in flight, as a result of aerodynamic loads).
Once all of the above has been confirmed, slightly adjusting the shape of the flaperon trailing edges is very effective in adjusting out minor amounts of roll imbalance.
BTW, I would expect that anyone that resorted to adding an external trim tab to a flaperon to adjust roll trim, would have a change in roll trim when they deploy the flaps. Every time they deploy the flaps, the trim tab angle changes relative to the airflow. It is no different than if someone were changing the bend angle on the tab, every time you moved the flap handle. A tab attached to the bottom of the flaperon and bent downward would be the worse case of this.