actually according to JSF spec - ajax behavior - not an action component as support was in 3.3.3 and parent component action/actionListener or value/valueChangeListener should be used to trigger business logic. But any behavior provides behavior listener which should be fired when Behavior event risen so something like that could be used in that listener

    public void listener(BehaviorEvent event){

        FacesContext.getCurrentInstance().getApplication().getNavigationHandler().handleNavigation(context, fromAction, outcome)

    }