Hello and welcome to just answer. I'm Dr. Gregg and I will try to help you today. While I am not a board certified avian expert I have kept and treated birds for 35 years. The first thing that comes to mind is that the youngsters were startled somehow and damaged the feathers by falling off the perch or struggling in the nestbox.
It may be best to move the nest box down near the bottom of the cage, along with the perches, then wait for the feathers to regrow.
There are a number of other diseases and virus's that can cause feather problems but usually come with other, more severe symptoms. If the budgies seem fit and act normal, odds are it is just trauma and should self resolve with changes in caging. If other symptoms are present then I would suggest a visit to an experienced avian vet for evaluation and testing.
Good luck with your budgies and if you have further questions feel free to ask by using the reply button.