Missing $current_user and $current_site globals when browsing mapped domain

I just noticed a strange bahavior while debugging an issue with the WP Maintenance Mode plugin.

WP Maintenance Mode allows you to set a user role that gets access to the site when it's activated. When I accessed the site via the mapped domain I was locked out. When I tried again using the original domain everything worked fine.

I had a look at the $current_user variable and it turned out it's empty. Same goes for the $current_site variable.

This would also explain why I don't see the adminbar when I'm browsing the mapped domain.

My goal is to only use the original domain for the admin + login/registration and the mapped domain exclusively for the frontend.

Can somebody offer me some help?