You have found the issue. Create new mailboxes (Inbox, Sent and whatever other folders) under "On My Mac" and save (move or copy) your Outlook.com account emails to those.
You can then delete the Outlook.com account from System Preferences>Internet Accounts and then add it back as either an IMAP or Exchange type. You can then copy your emails back from the folders under "On My Mac" to the proper ones under the new account. You may have to create new folders if you have any such organization. Once you copy the emails they will begin to upload to the server…this will take a while if you have a LOT of email.
You should start seeing the emails on your iPhone once the copying/uploading begins.
Once you've confirmed that all your emails are copied and uploaded to the Outlook.com server you can delete the folders you created under "On My Mac".
By the way, you can see the setting where emails get deleted from the server one week after the Mini's Mail downloads them. When you set up as IMAP or Exchange that won't happen anymore.