The Wired Reflexes/Reaction Enhancers combo is different, because those state that they're incompatible with other Reaction (and Initiative, for Wired) augments. (It's Augment-specific for Wired Reflexes by the way - so Wired still stacks with spells and drugs, but Reaction Enhancers don't stack with any other Reaction enhancement).
You don't get an initiative of Reaction (+3/+1)* + Intuition + Dice. You get an initiative of Reaction + Intuition + Dice. Whatever your reaction is, that is used for the calculation, however you reached that Reaction. Because Reaction Enhancers and IPA: Reaction don't increase Initiative, and thus stack with anything that increases initiative - they increase Reaction. And it doesn't matter what that Reaction is made up for when you calculate initiative, because, once it's increased, you simply have a Reaction of X, and that's what you use for everything that uses Reaction.