In Outlook 2016 there is a major issue if you want to use IMAP as protocol – and it is still not solved.
Emails in Inbox will not sync until you do the following:
1.) Right Mouse Button on Inbox
2.) IMAP Folder…
3.) Select all IMAP Folders and quit abos – Confirm and OK
4.) Re-Open the IMAP Folder Configuration and link all folders again