I am not the right person to test MusicBee podcast-related issues, but reading the above:
I am impressed at how you've thoroughly investigated the problem and reported on what works for you and doesn't as expected.
(something rarely seen on first posts).
As such, it would appear there's a bug at play.
If this topic doesn't get moved to the bugs section of the forum for you in a couple of days, then I suggest you repost this there for further investigation.
Edit:
What would probably help further is a link to a podcast that updates as often as the above setting is concerned so that other users willing to test are able to.