MarkB
Legend
This does have an impact on gameplay.
Bob: I'm using Mantle of Command to move Fred behind the Ogre.
DM: [looks nonplussed] Okay, you [mumble mumble] and Fred, you're now behind the ogre.
Fred: Wait, what happened?
DM: I dunno, the rules just say you're now behind the ogre because he spent his reaction.
No, thank you. Not if I can avoid it. I hate situations like this and I'd rather just preclude them from occurring. In this case that means overriding "the rules" and not allowing the Mystic as written in the campaign.
The discipline says "allow". The ally is allowed to take the move - they don't have to. Whether it's due to the Adept's inspiring psychic aura giving the character an extra turn of speed or his psionically-enhanced air of absolute authority spurring him to extra effort is up to the individual player. Either way, it's not your problem as DM - the players are taking the action, and they can narrate it any way that makes sense to them.