I purchased a finch from the pet shop that had this problem. I noticed it a day or so after and took it back to the pet shop. They refunded my money.
Everything has been fine since this happened over a year ago. Recently a batch of chicks were hatched with those awful sacs of yellow bumps and they parents tossed them out of the nest and i found all of them dead on the bottom of the cage. A few days later, one of my adult cinnamin finches is missing a lot of feathers and has the beginnings of it so I have separated him into a smaller cage on his own.
I keep the cage clean, they have a good diet etc so I really don't know what is causing this.
I've heard some people say it's normal, but I've seen other baby finches and they do not have those yellow sacs at all.
Did you get to the bottom of it?
I'd like to know. I've given my male finch antibiotics. If you found out from a vet, can you tell me what it is and how to treat it?