Wooden Double has the Manipulate trait and so would trigger a Reactive Strike. The question for the caster is would it be better to mitigate the critical hit and see how the Reactive Strike plays out. If the caster believes the critical hit was due to a very high roll, it would probably still make sense to cast Wooden Double. However, if the attacker can frequently land hits and critical blows, you probably would not want to risk the reaction.
As for Unexpected Transposition, it has only a verbal component, so it would not trigger a Reactive Strike, which needs a manipulate or move action to trigger (or some other conditions that don't pertain)