Contacts added through the iOS contacts app aren’t known to Outlook and therefore don’t synchronize back to the contacts folder in the user’s mailbox. Originally you could only add, update, or remove contacts through Outlook desktop or OWA, but in 2017 Microsoft added the ability to add, edit, and delete contacts through mobile clients. However, in this scenario, Microsoft recommends that contacts for an account are only saved on one device as otherwise the potential for contact duplication becomes very high.
One advantage of storing contacts in iCloud is that this handles contact synchronization with multiple Apple devices (for example, an iPhone and an iPad). In this case, Outlook synchronizes contacts to the contacts app and the contacts app then synchronizes to iCloud. Outlook for iOS needs a synchronization target to get contacts to the native contacts app. In any case, to set the context for iOS, we know that synchronization of Outlook contacts is one-way from Exchange Online to the device. I can’t say if the same thing happens in Outlook for Android because I have never used that client (in anger).
But one thing that hasn’t changed is the frustration of multiple contacts in Outlook for iOS. Lots has happened since, especially to expand the functionality of Outlook mobile. I last wrote about managing contacts in Outlook mobile in March 2017.