Contacts can be sync'ed when the account is added as Exchange.
- IMAP and POP3 is mail only.
Does this help?
Did you add the Microsoft account as an Exchange account on the phone?
The instructions regarding server names are found on:
Tap 'Set up an Outlook.com or Office 365 account manually'
Or you may consider install some of the Microsoft apps from the Play store:
(The built-in Gmail and Calendar app on the phone can be deactivated).
Or the contacts can be exported from outlook.com as .CSV from 'Manage' in the top bar at the outlook.com website, and then imported to your Google account.
This seems to work.
The trick is: if you choose exchange, you have to go for the manual config, else you end-up in IMAP ...
Thanks for your help!