Hi there! First, welcome to Pet Talk! Second...are you sure he's not eating?

I remember that when I first got my tiels, they didn't eat either...for the first week or so. Actually...they didn't eat 'in front' of me, or anyone, and that was probably due to the stress of being in a new environment. Their seeds were 'shelled' at night though, when I changed their food, so I knew they were eating something. It could be that because of the stress of being in a new home, and around new people, he might be scared and may not be eating in front of you. Cockatiels often eat little when they first arrive in their new homes.

He's probably pooping when you take him out due to nervousness. My lutino cockatiel, Popcorn, used to do that when we first got him.

Are his poops 'normal'? That in itself could tell you a lot about the bird's health, and from the frequency of the poops, you should be able to tell if he's eating. Is he active? Does he appear to be healthy/well fed? If he looks okay and is acting normally, he probably IS eating when you are not watching. I'm sure he's drinking too........I didn't see my birds drink at all for the first 2-3 weeks, but they were. They just had to feel comfortable to eat and drink when we were around. What are you feeding your bird? If the food you are offering him is different from the food he is used to, that might be the cause of him not eating. Birds need to be introduced to new foods gradually. If you are concerned and feel something might be wrong, or if you notice anything wrong in the bird, then a trip to the vet should be in order. Hope that helps!