I have now carried out a test with a dummy feed an can tell you exactly what happens when you subscribe (I can't say what happens on the Store page as that would involve submitting it, which obviously isn't practicable).
On subscribing, the top line shows the title of the podcast. The description column shows the 'itunes:summary' tag in the top section (not within an item). When you click on the 'i' button (without expanding the display to show the episodes) the pane shows the same 'itunes:summary' tag contents followed by the 'itunes:summary' for the top episode.
When you expand the display to show the episodes,and click the 'i' button on the top line you get only the 'itunes:summary' tag in the top section.
For each episode listing, the 'Description' column shows the 'itunes:subtitle' tag for the episode; when you click on the 'i' button for an episode you get the 'itunes:summary' tag for the episode.
I don't know whether this is a change from the previous arrangement, but the 'itunes:subtitle' tag works for the episodes.
This doesn't accord with your observations, but I did work through this carefully. I suggest you could experiment by making a duplicate of one of your feed, changing all these tags so that the content is the name of the tag, uploading the test feed to your server and subscribing manually in iTunes from the 'Advanced' menu (none of this will affect your real podcasts) so you can see exactly what is happening.