While PSC does protect custom post types (it dynamically gets a list of all registered types from WordPress, then applies protection to them), this seems like it might not be working since WP Publication Archive uses custom behavior, not just a custom post type. This might not be fixable, and here’s why…
PSC will check if a requested post (of any type) is protected, and then (if it fails the security check) remove the post from the data array before it is processed by WordPress.
In this case, WPPA probably checks for requests of the specified type, then runs a custom query to fetch the file data (which is not default WP behavior). Any time a plugin relies on a custom query instead of the default WordPress wpdb data object, there is absolutely no way for PSC to know about it nor is there a way to modify that behavior.
Basically, in order for the WPPA content to be protected, the WPPA plugin would need to be modified to use some of PSC’s security checks (it’s not just a custom post type, it’s completely custom behavior).