@panther Very cool @Panther, I knew you would have managed (that was exactly my belief as well, but I'm no krieghund, and I definitely believe that, while it might have been mostly indicated by the rules, they are really far from clear).
So, now all relevant is mostly clarified (and my memory was right yay...), and "only" need some developers to fix it. Summing up the bugs are:
What the engine does:
It resolves the AA flyovers immediately, to the extreme of letting you do, not only part of your moves, but even only part of a move for a same unit, see the AA flyovers, then use whatever movement you didn't yet use of any units, even comprising already partially moved ones.
For Revised LHTR:
It should, instead, tally all the flyovers each air unit or group of air units is making, then resolve them, together with the eventual AA fire in the attacked territory, during the first Opening Fire step of the Conduct Combat phase for the battle.
For Revised OOB:
It should, instead, tally all the flyovers each air unit or group of air units is making, then resolve them at the very end of the phase where they happened, after all your movement is done, mainly the Combat Move phase and the Non Combat Move phase (in TripleA terms, right after you click on Done to finalize all your movements). Theorically, it should also let you decide the order in which you resolve the various groups, but this may be relevant only for a Revised OOB based custom game, as in Revised OOB you don't have any advantage in choosing such order.
Remaining item for Revised OOB:
Since in Revised OOB (but not in Revised LHTR) the remaining movement of air that took part in a battle is done in the Conduct Combat phase (currently not supported by TripleA), not in the Non Combat Move phase, I'm not entirely sure when exactly that should be resolved (after the specific battle where these air units were involved or all together at the end of the Conduct Combat phase?).
Remaining item for Revised LHTR:
Since it was clarified that the way you assign AA casualties is by rolling separately all shots for fighters and for bombers, then taking out the resulting fighters and bombers casualties (that means you will take out the ones having the lower remaining movement first, instead of this being completely random, as in the case you would roll a dice for each plane singularly), what should, then, happen in the moment you may have to tally up the AA flyovers from the preceding Combat Move phase, and some of those shots were specifically assigned to aircrafts with a bigger remaining movement left? Must you, in this case, roll them before and separately from the AA shots you would be rolling for the AA that are in the embattled territory?
@Panther Please check if I said anything wrong and, if so, I will edit it (or feel free to edit my post yourself).
At the very least I hope this will end in some agreed and confirmed tickets being tracked in GitHub, and not being once again lost overtime... If not fixed, this matter should be fully and clearly documented and tracked forever, so that at any point in the future people may know the truth.