So there are actually two mail functions in the software. I'm so sorry this is unclear.
The system only sends actual emails for:
a) Control Room "Test Email"
b) Control Room password recovery
c) Patron password recovery
d) New Tenant/Organization created to the admin user of that Tenant/Organization
Everything else referred to as "Mail" is part of the in-system mail function. At the top of the patron screen there's an envelope icon which will show a little indicator next to it when a patron has unread messages. When patrons use the in-system mail function to send an email to administrators, you'll see it in the "Mail" tab of the control room.
I don't believe it sends an email for a new Control Room user.
The in-system mail system was developed so that email addresses of librarians managing the summer reading program wouldn't have to be given out (so that their email boxes wouldn't be overwhelmed with patron questions — our program has 77,000+ participants and we receive between 5 and 20 of these in-system mails a day). Our services team has a daily task to log in and check the mail tab in the Control Room to respond to patron questions and concerns.
I have task items to try to figure out a more intuitive way to handle this (possibly having people get emailed when they have a new in-system notification that remains unread for
X days, possibly having a checkbox where Control Room users can have in-system mails forwarded to their email) but I haven't gotten there quite yet.
I hope this clears it up, let me know if you're seeing behavior that doesn't follow those rules or if any of this does not make sense.