Organizing and accessing contact information in Outlook.com
I've had the same problem, but found the solution.
Just add your outlook account the regular way, no contacts will be added at this time.
BUT, now go to Settings/Accounts & Passwords and at the bottom you will see "Fetch new Data" and it will be set to "Push"
Click on that, next click on Outlook and change the "Push" to "Fetch" and all the contacts are downloaded.