Will the top layer of moist newspaper be eaten by worms or should I move it up when adding a new tray?

Since newspaper is food for worms, your worms will begin to break down the newspaper layer on top. If they do, just moisten another layer of newspaper and put it on top of the first. When you’re ready to add a new tray, just move the newspaper up to the new tray and continue feeding as before underneath the paper layer.