Hello, welcome!
First of all, as far as I know, your Apple ID being the same as one of your emails has nothing to do, they are separate accounts.
Second, if you added your MS account by going to phone settings > accounts and passwords > add an account, it should give you the option to toggle on/off 5 settings: email, contacts, calendars, reminders, and notes. Toggling on the contacts should start syncing and showing them in your contacts app.
Third: keep in mind that if you open the contacts app and check the upper left corner that says "groups" you can see if your outlook contacts are checked (hence shown) or not.
Hope this helps, otherwise, let us know.
10-29-2017 09:50 PM