Apparently, the problem is that, for some reasons, some units spawned with custom objectives are not used by AI commander... RHS strikes again... Yet, if they come from MIL or CIV placement modules, no problem, they do their stuff...
Basically:
The AI Commander had "no units" close to the objective, so he sent a unit he had control over... But this unit was on the other side of the map.
Since I only had Custom Objectives (since Celle 2 is having issues) and also to simulate an airborne staging point, the AI commander couldn't use most of 'hem.
Once I used MIL and CIV placements instead, all units were properly used.