CBroda,
May have found a resolution to your issue.
If you set the default group on your iPhone to your Outlook account, in Settings>Contacts>Default Group...
Then all new contacts will show up seamlessly. If you want to move old contacts, then you will need a contact mover application. They can be found on the app store, and it was worth the few dollars it cost.
Figured this will help you, or anyone else trying to fix this issue.
This resolved my issue. However, the location is a little different on the iPhone 6s. I also had to choose my company's mail server account name rather than just Outlook. As in iPhone, Settings>Contacts>Default Account>
I then had three choices - Outlook (default), iCloud, and "my company's account name".
The existing choice of "Outlook" was not correctly populating my Windows 10 PC company Outlook contacts, so I then chose my company's account name from the list on the iphone Settings>Contacts>Default Account> and after about 1min, my iPhone contacts were
now populating in my Windows PC Outlook contacts.