In that case, the reminders would be sent either at the top of the next hour, or at the top of the next hour after the time you entered the event plus the reminder interval, whichever is later. Reminders won't be sent immediately when you save the event in either case, so you won't see the confirmation message in your browser.
Example 1: You enter an event and select Require Acceptance on Monday at 1:30. On Wednesday at 4:30, you edit the event and add a reminder interval of 72 hours. The first reminders won't be sent Thursday at 2:00, because it hasn't yet been 72 hours since the original notifications.
Example 2: You enter an event and select Require Acceptance on Monday at 1:30. On Friday at 4:30, you edit the event and add a reminder interval of 72 hours. The first reminders will be sent at the top of the next hour -- Friday at 5:00 -- because it has already been more than 72 hours since the original notifications.