These birds have just moved into a new home so everything may be "off" for a while. Maybe the tiel is eating less than usual, or maybe it's pooping more often than usual because of the stress. Just keep an eye on the situation to make sure the bird seems healthy overall.

It would be better if you can put them in separate cages where they can see each other but not touch. The budgie won't be lonely, and the cockatiel will get to keep its feathers.

I love your new tiel! He has a great face, serious but curious.
Love the pic with the dishevelled crest

Me too!

Sounds like you've solved the problem...
So pleased for you and the birds...