If the feed does not specify a date, AntennaPod uses the date when the feed was added to the app. Contact the creator of the feed and ask them to include the date of the episodes.
What is the feed you are using if you don’t mind providing it?
It would allow other people to test as well.
Mainly it would also help to check if dates are really there and if they are included correctly.
Edit : missed it was for a private feed but still wouldn’t it be possible to open it in a browser and show a section about an episode and where published date is?