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A publisher Author should be registered through Publisher register form. Not all the joomla users are Publisher Authors, is not enough to be a Joomla user or a Joomla author, it should be a Publisher author which is something else.
So, you have two ways:
1. Go in Publisher admin, Author Manager (is under Authors menu) and make that Joomla users as Publisher authors
2. Create a menu on the site, from Menus, New - Publisher PRo - Author Registration - and let the Publisher authors register through that form.