Because the laws of physics demand that there must be a delay between the movement of a flight surface and the aircraft responding to that movement, as well as other uncontrollable external factors such as wind speed and direction, it follows that the pitch attitude commanded in a situation where the aircraft is slowing down will need to be somewhat shy of what it is at that precise moment - otherwise it risks encroaching on approach to stall, which would defeat the whole purpose of the protection.
Therefore, as pulling back in that mode cannot be assumed to give Alpha Max, what that sidestick command actually "tells" the flight control system is "give me the best AoA you can". So, going back to the beginning, the elevators were briefly commanded nose-down because the systems were trying to maintain the optimum (not necessarily maximum) AoA, and that was what was required to maintain it.
Laws of physic don't request much time : As freefaller we are used to modify the position, to feel on the body the aerodynamic forces and moments created, and resume the movement in less than 1/20 second. Not the tens of seconds of the phugoïd low period. An aerobatic's plane needs a longer time than /20 second but is reacting very fast. What needs time on your plane is the result of cheap and low sampling (perhaps to avoid high frequency transient response?) or a bad model and algorithm specialy near the stall.
And what is optimized? Cost as usual?
It is often question of "time needed" but no figures are given. The expert Max Venet said during the Habsheim trial - answering to the President of the Court - "we don't know very well how long the aircraft needed to be less than 30 feet RA over the trees (before the runway threeshold, not after the end of the runway..) to get in flare - I listened and
understood that - what is sure is that he did not find in the hard- and software documentation and modification history the answer to that question.
I wonder too to see now the ref of 150 FT RA in the landing algorithm -Hudson- (and phugoid damping) which is much more than the most oftened read 100 FT RA or 50 or 30 FT : How could the crew and the Court know really how the system works?