We'll look into the timing issue.
As for airplane mode - the energy push notifications are handled through what's called "local push notifications." These are actually scheduled from the app itself, rather than being sent from our server. Since the game knows when your energy is going to recharge, it just tells your phone to send a push note later, and your phone queues it up and shows it at that time. That's why there's no internet connection needed for the out of energy push notification.