The text for handling damage in the Political Escort mission offers two different methods for handling critical hits to the shuttle in the same sentence. I don't have the book in front of me ATM but it goes something like "Change any # results to * results (i.e. deal all damage cards to the shuttle face down)" The first half implies a functionality similar to focus or marksman, changing critical die results to non-critical during attack modification step, before agility is rolled. The second half in parenthesis seems more akin to Chewbacca's unique skill, flipping face up damage cards face down immediately without resolving their effect.

In most cases this is irrelevent, except if you're using the squad builing variant. If I wanted to put Draw their Fire on one of the escort ships, and it works like the first half of the sentence implies, DTF is useless, since there will be no uncanceled critical hits to draw away. If it works how the parathetical implies, DTF becomes a cheap addition to extend the longevity of the shuttle and complete the mission.

So how is it supposed to work? Thank you for your time.

That makes sense. When in doubt, favor the standart text over the parenthetical. On a similar train of thought, if Backstabber gets an extra attack die when outside the defender's firing arc, does he get 3 red dice when shooting at a ship without a firing arc, like the senator's shuttle, or does there need to be a firing arc for his ability to trigger??

That question is actually covered in the FAQ: