I have to assume that thread originator found solution with Microsoft Support. Just wanted to add my 2 cents. Symptoms that you are describing are indicative of immutableID mismatch. During Federated Authentication two attributes are used in the claim, namely user's UserPrincipalName and user's immutableID. Out of the box immutableID is Active Directory GUID serialized/converted into base64 string. If Azure detects a mismatch of immutableID that Federation claim is carrying from AD and the value previously/currently stored in Azure AD it will either display an error indicating that there's no matching user account found (when attempting to login into portal.microsoftonline.com for example) or in this case redirect user to the Live ID/Microsoft Account login page, since Outlook.com is shared URL between LiveID/Microsoft Account and Azure ID/MSOL.
To fix this you will need to clear MOSL user's immutableID attribute. It could be done with PowerShell, if accounts have not been synchronized with DirSynced. (If you are still unable to remove stale immutableID, try deleting the account with Powershell or in admin portal and restoring it back). Having your accounts DirSynced could throw an additional variables into this equation, since you will not be able to simply edit an account or delete/restore it, but have to rely on your AD to perform those operation. You should contact support and let them guide you through the process of clearing out your stale immutableIDs from Azure AD.