In this case, the copilot seems to have remained the PNF (i.e., as far as we know there was no formal handover of control), but made sidestick inputs - whether intentionally or not.
A pity the CVR isn't available, there may have been a brief verbal exchange which would explain that. Seems out of place.
Chris, your estimation of the "chasing" of air data sensors by the A/P in such entries into turbulent air is confusing to me.
I learned a long time ago that if you were entering turbulent air that has a lot of vertical component, that you need to work on holding pitch and power for the proper "turbulent air penetration" airspeed. You could expect both A/S and altitude to vary a bit as the air mass bounces you about.
"Don't chase it!" was some of the teaching then.
Is that still current teaching?