I think it is important that before the second round starts to hatch, you clean both the nestbox and the droppings from the cage floor, placing clean sawdust in the nestbox. Another thing you should clean are the seed dishes and water fountain, making sure there is sufficient clean grit and cuttlefish.
Many people often forget the grit after the first round.
In my opinion, now is the time to give your birds any extra titbits they like, because they will have already fed one round, and you want to ensure the second round is well fed. Not a lot, but I find it stimulates them to come down and have a feed of seed and then go and feed the babies. I think the biggest problem we budgerigar breeders have been facing for the past 1O years is the decline in the percentage of fertility. People have all sorts of theories about why young chicks die when they are first hatched. I believe it's due to the hen not having produced enough crop milk.