At my previous employer (which features a large purple goat on the tail) it was SOP to set D2 climb as part of the FMGS setup unless particularly heavy - and it was very common for the guys to clear the derate and go to normal full power climb shortly after thrust reduction.
Sometimes with a heavy amount of flex on takeoff and a D2 climb set, there is virtually no change in the engine power / engine noise at thrust reduction altitude, as you move from the MCT to CLB detent.
I suspect the power increase you're hearing is not actually the "thrust reduction" move from MCT to CLB detent - it's a few seconds later when the pilots clear the D2 climb and it powers up to normal climb.