Hi, Natasha.
I’m thinking a few factors may be adding to the problem here, so have some suggestions. And no, sitting and watching them is not necessary, even if they make a mess again and you don’t catch it for a few hours.
First, the newspaper is confusing. I would remove it totally. You may find at first that it’s harder to clean, but it is a litter-like material and they may be opting for it. It’s good to remove all semblance of bedding outside a litter pan so there is not doubt that the litter texture is in the box, never outside.
If you are switching around litters, that could also be a problem, Bunnies are creatures of habit, like what they like, and that’s it. So, if your litter is wood pellets and they like it, the best thing is to use the same litter consistently. Have you tried Feline Pine pellets? It is liked by many bunnies, is safe, and is inexpensive, even in grocery stores. Untreated wood stove pellets are good, just try to stick with one brand. Yesterday’s News is a good pelleted litter. More expensive are Aspen Supreme pellets, my favorite.
It may be that they don’t like pellets as much as softer litter, so you could also try Aspen shavings, or Carefresh. Do NOT use Pine shavings or Cedar. Unsafe, as I think you know. If they like the newspaper, it may be that it’s flat and soft.
A fresh litter pan that is roomy is usually a good investment. Sometimes the old one just doesn’t smell clean anymore (to them) or has too much residual cleanser odor on it. My bunny had a great pan, but LOVED the much larger one I got her this year. She looks like she’s playing sailor in her big boat, and doesn’t kick out the litter, just messes it around when she’s feeling playful. I found it dug up this morning, put a fresh layer of aspen shavings across the whole top, and she jumped in to use it asap. They want their clean litter.