Draw their fire specifically says when a friendly ship at range 1 is hit by an attack, but Darth's crew ability says after an attack. IMO this means draw their fire cannot be used when Vader's crew ability is activated. The question is, is Vader's crew ability considered an attack?

Sorry if this has been posted already.

You have it right. Vader is not an attack, doesn't hit (required to use DTF), doesn't involve a [crit] result for DTF to transfer, and thus cannot be redirected by DTF.

Best way to keep track of it is:

uncancelled Results --> damage

Damage --> shields

If no shields, damage --> deals cards.