I have seen the mail app in my i Phone (4S, i OS 5.1) automatically updates the badge count if new mail arrives, even when app is not running.
However, later I became aware of this thanks to a friend.I use i for mail on OS X (10.9) and on both i Pad and i Phone (i OS 7.0.4). It only clears the new mail number and dots next to unread items after I make Mail the active window.When I read a message on one device, the message appears as new on the other devices. I thought one of Mavericks features was that alerts were cleared from other device's Notification Center.I stopped using gmail IMAP, but if I remember correctly, they didn't show messages as new on other devices after the message was viewed on one of the devices. When using IMAP, like i Cloud does, means if you read the message on one device it updates them all as read. Thanks for the clarification (although the issue appears to be with i OS as well as Mavericks). When using IMAP, like i Cloud does, means if you read the message on one device it updates them all as read. Resolution If your i Cloud email account is configured to use Push (in the Fetch New Data settings on your device), your i Phone, i Pad, or i Pod touch will update automatically whenever you receive a new message in your @or @Inbox.Minor issue, but this seems like a poor design or a bug, no? As long as it's 'known' and hopefully/presumably on a list of things to fix... However, moving an email to a folder, reading a message, or flagging a message does not trigger a push notification.