Did you get the Office 365 password prompt or the Exchange on-premises prompt?
If you get the Exchange on-premises prompt, this phenomenon may related with the Outlook Anywhere or MAPI protocol for your Exchange server. Make sure you have configure them correctly.
If you get the Office 365 password prompt. If you are have a hybrid lab, you could have a check about this KB: Outlook prompts for credentials for on premise users with Office 365 client. If you don't have a hybrid lab, try to update Outlook to the lasted version and try again.
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