I was wondering the same. I had a few budgies with the same spots, but they all went away with their moult. I do not know what causes it. One was a sick baby then, she got on medication and got healthy, but the spots went only with her first moult. The others were not sick as far as I and the vet said, and the new feathers are spotless.
I wonder if anybody has any information about this.
I think the black spots are related to stress while the feather is growing in. My blue crown conure got those when she had to live with my mom for 6 months (I was flooded out of my house). As soon as I got her back and her stress level decreased, the feathers started growing in normally again.
Hi. Sara. When I had my buster he was the same colour as your bird he got black spots on him and my mum said that is new feathers coming through when the new feathers came through the black spots went away. Indi gets them on his head when he is moulting when the moulting is over the black spots go away. Unless he has mites they are black. I have seen mites. But I think it has to do with molting. Ask your budgie vet if you are worried. Lyn and indi