Consider User A is accessing his mailbox along with another user's(B) mailbox. User A has the manager or Editor access over user B's mail file.
If any user marks an email to both these users then mail immediately reflects in User's A mail box but when he checks User B's mailbox, it doesn't download immediately. It arrives after manually refreshing the mail box only.
There should be a functionality to automatically download the mails for both the mail database.