Hi and welcome! Your in the right place to learn about tiels.

Congrats on bringing your Baby home. You mentioned he just came home recently so he's probably not use to his new home. That's ok. As far as the biting and becoming "mean"-yes, after they get a little comfortable, just like kids they like to test their grounds and see who's boss. He just wants to see if biting makes you go away-simply put. There are alot of way to deal with that. Males in general , esspecially adults, tend to have these little mean streaks then overwhelmeded by immediate sweetness. It's quite odd. You mentioned he is not afraid of cats or dogs, I'm assuming you have a cat and dog so just keep in mind he shouldn't be unsupervised around them if he's out. He probably is very use to his last owner just keeping the cage open-I do the same but I don't have other pets around. I would give him some time, try having him step up on your finger by placing your index finger under his belly and saying up. I'll look up a few links that might help you with him.
This shows common behaviors of tiels: very helpful guide:
http://www.tailfeathersnetwork.com/birdinformation/behavior.php
This one is one biting issues:
http://www.birdchannel.com/bird-beh...-behavior-issues-biting/why-parrots-bite.aspx