It sounds like you are trying to subscribe for other users. That can't be done (as far as I know) because SPS bases some part of the subscription on your login ID. So you end up creating a bogus subscription. Users may still receive notifications... I am not at work, so I can't test right now and give good specifics, but their subscription listings (in the subscriptions webpart and on the subscription dashboard) won't show the subscription because SPS doesn't resolve the subscriber from the SMTP email address you provide.
You said you were inviting users... how are you doing that?