Are you sending the emails from an email address that belongs to someone other than the sysadmin? Does that email address belong to someone who has author permissions on the site?
The way the plugin works is, it compares the sending email address to the accounts on the WordPress site, and if there’s a match AND the user in question has posting rights, the author will get set to that person. If there’s not a match, it gets set to the admin (and set as “pending” instead of “published”). My first guess would be that the latter is happening — the email address you’re sending from isn’t getting matched as a WP user.
To double-check, go to the profile for the non-admin user and verify that their email address is the same one you’re sending FROM.