I wonder if the problem only occurs if you are in an enterprise context and your UPN is not the same as your email address. In my case, if the system sends mails to my UPN, i will never receive them.
Here is some more of what I found out:
Using a "Alternate E-Mail-Address": In an enterprise context, I'm not able to set and use an alternate email-address as suggested here. That's because I'm not allowed to change my information settings due to organizational reasons.
But IF i could, there's another problem: According to our AD guys, the "Alternate email" information is stored in an AD-field named "othermails", which can only be set in the Admin-UI if the user got a special role assigned to. But that does not apply, if the user is a simple PBI-User (and no PBI-Admin for example). So putting email addresses into the "alternate email" will fix it only for special users.
Additionally, the "othermails" field doesn't seem to get synced from AD to the AAD. That means that putting email-adresses into that On-Prem-AD-Field wouldn't change a thing for the cloud service.
If the Power BI-function that sends alerting notification uses either the UPN or the "othermails" field, emails get lost. There's a AD field called "mail", which could be used, but perhaps it isn't, at least in some cases.
Sorry if some of the information above is perhaps specific to our case. (after all I'm a BI guy, no AD expert)
If I simply missed something - any help will be appreciated!