I've searched around for this a bunch of times and haven't found a straight answer. Problem: I read an email on my mac using mail.app, but the red badge on my iPhone won't update. For example, if I have two unread emails on my mac and read one of them, the badge on the iPhone will remain at 2. But when I actually open the mail application on my iPhone the application refreshes and recognizes that I've read the email. This behaviour seems more like "fetch" than it does "push."