With the last update, the issue no longer occurs and AI on deck will taxi and take off while other AI are holding overhead. I didn't see anything in the changelog regarding the issue but I'm glad it's gone!
There are no problems with any control layers or any "concept issues in the code". There is a fundamental difference in how the AP behaves in the Hip and the Hind. In the Mi-8, the AP servos are unaffected by trim while in the Mi-24 they are reset to zero whenever the trim button is pushed. So imagine you are hovering and just found the sweet spot for the cyclic. Before you trim, your total input is your stick position+whatever the AP puts in (which can be up to 20% IIRC). When you press the trim button, the AP input is "taken away" and your total input is not what it was before trimming, even without moving the stick. That's why it is important to trim a lot and thus minimize AP input, especially when transitioning from/to hover.
OPs video showcases that. If you look at the AP indicator in the top right corner, you will see that there is both pitch and roll input from the AP . As the trim button is pressed, AP inputs return to zero, changing the total control input.
Now one can assume that this behavior is exacerbated by the AP inputs being too large in the first place but thats hard to tell without knowing exactly how the AP works (which ED should and we have to rely on them getting it right). There are issues with the FM in general though, most prominently the uncommanded pitch oscillations at approx. 120-150 kph (SAU on or off) and IIRC ED stated that the FM and AP will get revisited during EA. But don't expect the trimming behavior to be the same as in the Hip/Huey.
sLYFa's post in [ST/MT] Carrier departure/arrivals: AI orbiting in the stack block departing AI was marked as the answer