Noticed this bug the last few weeks. It seems to affect movies more than tv shows for me. In fact, every movie. Even if I let it play all of the way to the end of the credits.
Like the OP, the continue watching hub shows the entry with just a few seconds left of play time, and asks if you want to watch from the few remaining seconds it sees there.
I’m not sure if this started to happen after a server upgrade or app upgrade. I would guess it is probably related to the move Plex has to combine Continue watching and On Deck.