To clarify, the "moving up action" is more a gesture you make with the cards to make it clear to yourself and your opponent, which cards on both sides of the table are currently participating in the engagement.
So, in the OP's example, it would go like this;
I declare an attacker against your Objective
You play Jedi Mind Trick on my attacker
Option A: You declare no defenders, the attacking unit cannot focus to strike and thus wins edge by default. I could play edge cards, either to clean out my hand or dump a Target of Opportunity in there to add a damage to the engaged Objective. After that, since it's an unopposed engagement, the engaged Objective would take 1 damage.
Option B: You declare a defender or defenders. Edge battle happens. After the edge battle, my attacking unit sits there powerless with a Focus token, and you resolve your defending strikes.
Either way, the engagement still progresses, but the Focus'ed attacker cannot really do much other than be there for unopposed damage, or get totally wrecked by a defending unit.