How to use Microsoft Exchange ActiveSync to sync Hotmail and Outlook contacts to Android?
Have you tried connecting another Android phone? It would be a nice AB testing to see where's the problem. 

The first answer that comes to mind is to check whether your contacts not set to sync with Google contacts. In some cases that prevents everything from working correctly.

Another solution is to enable syncing email alongside with syncing contacts. Some Android phones don't update other data correctly till emails syncing is turned off.

And the last option is switching to the software called Akruto to check if that could fix everything. You can find all instructions and video guide on the official website: http://www.akruto.com/best-ways-to-sync-android-with-microsoft-outlook/

Hope this helps!