Are your birds at least 2 years old? You mentioned they had been together for about a month, but it is important that they are at least 2 years old before you let them breed. If they are not that old, I would recommend removing the nest box until they are 2 years old.
If they are old enough, I would make a couple of changes with the nest box. Go ahead and remove the paper towels and shavings. Paper towels are not good for nesting because they mold very quickly once they get damp. As for the shavings, you should only use aspen shavings – the kind sold for small pets, all natural with nothing added. Other types of wood shavings have too much dust and aromatic oils that irritate their respiratory system and can even kill some birds. Your birds will most likely kick out all of the shavings – for some reason, captive breeding cockatiels rarely use nesting material of any kind. It would also be best for you to go ahead and cut an opening in the cage for the box opening, or buy an actual breeding cage, which will have a small door for the nest box opening. With the box inside of the cage, you have no easy way to monitor their progress. It will cause too much commotion each time you try to check for eggs or chicks, so you would basically have to wait and see if it all turns out. With the box on the outside of the cage, the top should lift, and then you can peek inside to check for eggs or chicks or make sure the chicks are being fed. Depending on the type of wire for your cage, you may be able to cut a flap that folds back. If you have to cut it and remove the wire, then you would have to block the nest box hole when they are being rested from breeding. They should be rested with no nest box access for 6 months after each clutch, whether the eggs hatch or not. The female loses calcium and protein when she forms eggs, so she needs time to rebuild her resources between each clutch.
Thank you for asking Lafeber,