The only way I could get my Outlook.com contacts to sync correctly with my Droid Turbo 2 is to:
1. Use the default email client, and set up a corporate account.
2. Or use the Nine app from the Google Play store which costs $9.95 after a free 10 day trial.
The official Outlook app is a DISASTER as far as contact syncing. I also found that if one has the same outlook.com account attached in more than one app, then contact syncing is also a disaster.
It appears to me, that the built in Google EAS sync is seriously flawed as someone told me in another forum that Google won't give 3rd party apps permission to use its EAS sync. Shame, Shame on Google if that is the case....