Indeed, these sound like red mites. As you just discovered, they turn red at night when they feed.
Feather mites are much smaller --- so tiny you don't generally see them moving.
Vaseline scares me, as it would require dish soap or similar to cut through the vaseline. And if you don't remove it thoroughly, it will cause the feathers to clump together, chilling the babies.
You mentioned they were 4 weeks old. Are they fully fledged? I know they typically fledge anywhere from 4-6 weeks. If necessary, I might wait a few days until they're fledged.
This is a very tricky situation because you must clean the environment AND the birds very thoroughly. But removing a nest box and cleaning it so thoroughly may cause the parents to reject the babies. But if they're fully fledged, the chances of a problem are decreased as you can technically eliminate the nest box after fledging.
I would definitely have some handfeeding formula on-hand too, just in case the parents abandon (though if they're very tame parakeets, they tend to be more tolerant of interference than a more aloof bird like a finch or an un-tame 'keet.)
Those mites can cause fatal anemia in very short order in little ones. They've likely had them for their entire life, which means they're already weakened so I would treat asap.
If the babies are adult sized, they should tolerate an adult dosage.
By 4 weeks, most species have finished growing for the most part. At this point, it's more behavioral maturation and smaller changes, like molting into the adult plumage.
So since you don't have the rapid cell division as in the case of a growing baby, there's less risk that a drug would have an adverse impact.
I would use a standard product, such as AIL.
http://www.finchniche.com/product_ail.php
It can also be used on the bird and objects, like the cage, perches, etc.
You must treat the area around the cage too.
I would vacuum, then spray down any carpets and wipe down all surfaces in the immediate area.
If you happen to have a blacklight, peek at the area to see if these critters glow. If memory serves, I believe that red mites glow under blacklight.