Disabling plugin for logged-in users

I have recently installed Super Page Cache on a site that uses PaidMemberships Pro to offer unlimited content access to paid users. Free users / non-logged-in users have access to five posts a month, and after that are redirected to a login screen.

Normally, the redirect to login includes a URL parameter to send the user back to their original content after logging in. However, since enabling Super Page Cache, this is no longer happening.

My assumption is that the cache is still applying to these users who are now logged in, so something in the redirect is getting messed up via cached versions of pages.

Is it correct to assume the front-end pages would continue to be cached for logged-in users?