After activating your tunnel, you must stop/end/quit Plex server and restart it, because only then will it be able to report your new external IP address to plex.tv immediately.
plex.tv in turn will perform the accessibility test and will also tell your new external IP all other plex clients which have access permission to your server.
The alternative is to wait ~ 1 hr until plex server will update the external IP address information automatically, or to create an exemption for plex server from the VPN altogether: [How To] Bypass VPN for Plex
