The Actions app allows for a two-step action process, allowing an administrator to define which visitors are allowed to take an action. In this process, the administrator sets the Who Can Act filter, and the Actions app limits the action only to users that fit within that filter. Unless the Who Can Act filter is set to "Everyone", visitors will always need to enter their full address (including zip code, but not requiring a +4 zip code) to move to the second step.
With that in mind, at this time, an action cannot use only the visitors zip code for district matching.