Media files are always streamed directly from the publisher’s servers when using a Chromecast device. Once the app communicates with the Chromecast device to start playback, DC isn't involved any longer until playback completes or you hit a button in DC.
To resolve most playback issues:
1. Exit & restart the app (DC Navigation Menu>More>Exit) then press the Chromecast icon and play an episode from the podcast with the playback issue
2. Reboot the Chromecast device.