I have seen the episode, so I already know where the green time rings come from: one for each new timeline/parallel universe created because of time travel to the past. My question, which others have made and the link in the OP doesn't really answer; is where does the assumption that all drawers contain more time ring comes from? Because I've seen nothing indicating that in the episode. In fact, the box used is the same box that was shown in the previous episode, containing one main ring and four additional rings that indicate four parallel universes/worlds. Wouldn't it make more sense to invite Beerus and Whis to the vault and show them the drawers if those truly contained more time rings?
So far it seems to me that each World has a single grey Time Ring and additional green rings for each parallel world. And while there isn't proof of separate timelines for each universe so far, there are some things that could hint otherwise. I'm not actually arguing for a single time-continuum, since I have no proof either way, but I don't see where this assumption for the drawers having thousands of additional green rings comes from. In fact, Gowasu's words indicate the last green time ring that appeared did it in the small box he showed Zamasu. Shouldn't the small box be already full if there were thousands of previous green rings, making it so that new green rings would appear in new boxes in other drawers?