With an engine failure at or above V1, TO performance for a fixed derate is based on NOT using any added thrust -- use of added asymmetrical thrust may take you out of the protected VMCg. With an Assumed Temperature thrust reduction, additional thrust MAY be used.
Points of note -
(a) neither derate nor FLEX require any pilot adjustment of thrust in the event of a failure ie, the normal RTOW calcs are predicated on the thrust level set at the start of the takeoff.
(b) FLEX will/derate may tolerate an increase in thrust on the operating engine - caveat - do it SLOWLY as there is a risk of a thrust overswing depending on the engine control systems. In any case, at a critical stage of flight, the handling pilot doesn't need the additional complication of having to dance a jig on the pedals to keep the aeroplane more or less straight while the lever is being pushed up.
(c) Vmcg/a should only be a problem for a very lightweight takeoff at, or near, min speed schedule. One of the saving graces is that the light aircraft typically will be accelerating rapidly and, by the time the pilot increases thrust, the actual IAS will be somewhat higher than what the takeoff was predicated on.
(d) It still is presumed that any adjustments by the pilot will be such that the rated (or derated) thrust level is not exceeded.