Hi Dan. Yes they do but thats a ground check sequence. Try and find a video with the flapperons moving at all during the landing. You'll see the tailerons move much more than the flapperons do even with their one wheel rolled attitude landings. http://www.youtube.com/watch?v=ez34sKSye3Q http://www.youtube.com/watch?v=55c4o...eature=related
In flight they both move controlled by the FCS but again if you observe many of the manoeuvers, depending on the velocity the tailerons move a lot more than the ailerons do even for roll input.

I don't know if you looked at the continuation of my conversation with Kevin but re Elevators and tailerons one question I finally asked was why do stab/elevators make such poor roll surfaces on models. He pointed out the concern of that the taileron can better manage the aircrafts AoA. I'm still trying to formulate the actuals but with the Pitch surface much closer to AC and CG proportionally place between about the NP, the force requirement is reduced but the drag is less and the ability for it not to be blanked by the wing since it has a wider range out of the wings flow is additional reasons beyond sonic for using Tailerons.

When this is incorporated with the use of flaps/flapperons where more pitch and roll authority is required with less drag in a turbulate config the taileron is the easier but both can work if the aircraft is like an F-4 where it has dedicated roll devices and thus only requires pitch.

This OP is asking about the F35 which like the SU 27 Fam uses tailerons and depending on the speed and manoeuver, uses aileron roll or uses taileron roll. During the landings though, the roll again is loaded to the tailerons.