Am I correct in assuming that this is an action you do instead of another action?
So rather than use the x-wings actions for its own benefit, you instead give one evade to the shuttle?
Exactly so. Any rebel ship gains adds "protect" to its action bar, which it can chose to use instead of focus, target lock, whatever. This will make the X-wing less effective, but it will make the shuttle tougher....and if the shuttle escapes, it doesn't matter how badly hurt the X-wing is.
There is only the one x wing, and the tokens are removed every end phase..... so it's not that the shuttle can store those not used.
So how can there be more than one.
Probably something I'm overlooking here.
Because the rules also include provision for playing it with 100 point squads instead of just the two TIE fighters in the starter set:
(If playing with 100-point squads, it has a shield value of "6". Use tracking tokens to represent the shuttle's shields.)
If you're using 100 point squads, there is a real argument for a rebel squad consisting of 5 autoblaster turret Y-wings trolling along in a tight box doing "protect" every turn.... hurting the shuttle past 5 evade tokens is going to be really, really hard.
It's an interesting mission to play at 100 points. The "force awakens" core set has a similar mission - this time with a protectee that's not quite so tough, but can shoot back and gets a focus token.