Sony has wisely avoided getting into a semantics argument about the definition of "through" by stating a clear conclusion to the Welcome Back package: 9AM Pacific on July 5th. That gives procrastinators another day to do everything else but download their free games.
No, we're totally kidding. Go do it now! Not at home? Make a little mark on your hand to remind you when you get back to the domicile. This is it: no more reminders or extensions. Get it done.