Author Notification emails are auto-sent "TO" the author (or any role) that is being added to a submission. If I am adding Kendra to a submission, then the email will be addressed to Kendra. This is true for TEST and PRODUCTION sites.
The Author Notification email will also CC the 'current user'. This means if a submitter is signed in on the front end, that submitter is the 'current user' and will be cc'd on the Author Notification. But if an author is added from the Admin - Edit Submission, the admin account is the 'current user' and so the admin account will be cc'd instead of the submitter. Again, this is true for TEST and PRODUCTION sites.
NOTE: The Author Notification email must be set to Status = Active in order for the emails to be auto-sent.