We use rules in Outlook to move incoming mail to different folders. I have noticed that the mobile devices do not show a new mail notification for the messages that have been moved to folders. The folders do not sync mail until opened. I've spoken to O365 Support regarding this and am getting nowhere...
It seems like I've seen a setting before in OWA to tell it what folders to push to mobile devices but am not sure.
Any insight into this would be greatly appreciated.