If a user is already subscribed to the page, they'll get added to the sequence immediately. This has to do with how Facebook recognizes a subscription event.
A new user (somebody who is not already subscribed to your page), will not get the subscription messages right away (as they're not subscribed until they send a conversational action back to your page).
Here's a related video I just made about conversational actions, and what triggers a subscription event ->
Hope that helps!