When do the cards update?

By themselves. Every hour Podspun reads new episodes and posts (and any episode whose description changed) for every site with a Categories block, for all three of its categories at once, and the new items slot into the cards. Opening Site Settings, Content Categories starts a read right away. On a preview, only the sample episodes are read; after you turn the site on, the rest of your catalog is read over the following hours.

Switching to another of your three categories reads nothing again: every episode was sorted into all three when it came in. Only shows on a site with a Categories block are ever read, so it adds nothing for anyone else.