Login and private plugin

I'm only about 5 hours into gravcms with a site up and running.
I used admin plugin and login and private plugin.

The private plugin is meant to protect the whole site with a password. This however seems to conflict with the main login plugin - so instead of the private plugin running and showing its login screen, I get what looks like a login screen from the main login plugin.

Is there an order of precedence for plugin loading or this just a bug in private plugin. Happy to post on private plugin github too but dont know enought about the architecture yet to phrase my question.

Right there's some interference between the two plugins, the private plugin picks the admin plugin twig template. I made it work by renaming the plugins/private/templates/login.html.twig to login2.html.twig and in plugins/private/pages/login.md I put 'template: login2' in the page header. Waiting for a proper fix, this should make it work, let me know if not.

Thanks flaviocopes - just figured this out checked back here to post same solution :)
Awesome support - thank you - and really enjoyable first foray into grav