Re-check in Users & Groups in System Preferences and choose your User Account >> Tab called " Login Items " and see of Podcasts is in there. If Yes, remove it. This will stop the application from launching when the computer restarts or from Cold Boot.
That or make sure the Podcast application is totally Closed before restarting to shutting down computer.
To observe - when shutting down the computer and windows appears with the countdown to shutdown. Have you " enabled " Reopen windows when logging back in. If Yes, untenable this my removing the check mark.