Go to "Settings" -> "Auto Download" and make sure you uncheck "Playlist auto download" and select "None" in New Episodes menu.

Enter "Customize" section, check if the default option is "None" for all podcasts. If not, you can reset. Then go back and select "None" in New Episodes menu. Then it will apply instantly to all podcasts.

After logging out the app, the auto-download settings could not be saved; then when you log in the app again, the auto-download settings will be back to the default. Same case happens after you clear the data of the app.