Always verify that this is the issue by comparing items in Outlook Web Access with the i OS device, not Outlook. If there is a field called "default account", make sure it is set to the Exchange account. Existing local contacts cannot be modified to store them in the Exchange address book.
This will create duplicates for the local contacts.
The user will then need to go back and delete the original entry for each, or hide the contacts created locally to view Exchange contacts only.
The final piece of the puzzle: in File, Options, Advanced, you can set your "real" Inbox to be the default start up folder. After you set up the account in Outlook, move your appointments and contacts to the data file folders. If you are using an IMAP account in Outlook 2013, close Outlook and delete the IMAP account's data file.
When Outlook restarts, it will create a new data file without the special folders.
Set the account to be the default data file on the Data Files tab.
This puts the calendar in the To-Do bar and new appointments and contacts will go into it's Calendar and Contacts folder. If you want to remove the calendar and contacts folder from the your "real" account uses, see Delete Special folders.
To fix the [email protected] address, set the address as Primary. EXPORT the data to a PST file before removing the account from Outlook, especially if you have any new appointments or contacts that did not sync up.
All accounts have been migrated to Office 365 servers and all accounts set up in Outlook desktop need to be re-configured as an Exchange account. If you don't do this, you will lose them when you remove the account. What you need to do: log into with your Microsoft Account.
Create a "Microsoft Account" for your email address and use that in Outlook.