Podcast Addict uses the new Android 6 API, so Automatic updates can still be triggered while the device is in Doze mode.
The only limitation is that the update might occurs up to 15 minutes after the selected automatic update time (Google limitation).
Since Android 6.0.1 some users reported that automatic updates aren't triggered anymore.
As a workaround, you can disable Doze mode for Podcast Addict. To do so you can go into the device settings (Settings/Battery/Battery Optimization) and move Podcast Addict to the 'Not Optimized list'
This should solve the issue until I can understand why it doesn't work as intended on some devices.