Well I have played with it a little more. If the area one attacks during the first combat phase is still enemy-controlled at the end of the first combat phase (either because you just attack with air units or because there is a ground unit but it does not survive the attack), then during the second combat movement phase you can move a friendly ground unit into the area and then directly into another enemy-controlled area. Otherwise, you can move into the attacked, now-friendly-controlled area, but not then move from there into an enemy-controlled area.
Then I tried putting the second combat movement and combat at the very end of the turn, after the EndTurn phase and now it works, I can move into the previously attacked area (whether it is friendly-controlled or enemy-controlled) and from there directly into an enemy-controlled area. You cannot use air units to support any attack you make in the second combat phase (because they had to land during noncombat movement). But this does not bother me.
If anyone has a better way to do this please let me know.
Idk if the new pre auto centers now or not. Haven't tried it yet