Lots of good questions, let me see if I can tackle them one by one.
First and foremost, WELCOME!! You have come to the right place
lots of friendly people here willing to give you advice from thier own experiences.
The first is I've made a few mistakes in my ignorance and would like to know how to correct them. Examples are: my wife didn't know to leave the bird alone for the first few days
not too worry, he seems to have been somewhat comfortable with hands and he has gotten past the stage of getting used to the move so it's all good.
I introduced toys without allowing Tyr to get used to them first,
every bird is different. You will hear some users here say they set a toy beside the cage for a few days before putting it in the cage. Others, like myself, just put them in there. I have 4 boys and some of them will sit far away and look like I just put an alien in the cage, and others will run right up to it and show the new toy whose boss! When you get your next new toy (and oh you will get plenty of them!!) try the slow introduction and see how it goes.
Your bird is being relatively tame and comfortable so I don't think you have caused any problems.
he got out of the cage and it was a frightful expierence for him getting him back in
Aruba did this too. One thing that can help is if you have his wings clipped at first. If they are done correctly, he will still have some flight but not too much. He will need to rely on you to get back to his cage and won't be able to flutter around the house hitting who knows what. They will grow back and once he is more tame and bonded to you and your wife, you can have him fully flighted if you want to. (my 4 are fully flighted now)
and I've been using millet as an aid in training him.
Not sure why you think this is a problem? Many of us use millet as a training tool. It's just like giving a puppy a little dogie biscuit when he sits on command.
I'm kinda at a loss where to go next. He isn't quite hand trained. He will perch on my finger, but he doesn't seem to like it. He only stays for a short period and quite often he tries to get away from me
Just take it slow and easy. Don't press on further until he is even more hand tamed. When he sits on your finger allow him to eat a little millet. Talk softly to him and just let him know how crazy you are about him.
Whenever I approach Tyr, he fluffs his feathers and then shudders. It's more like a reaction to me than he's just trying to be warm. Anyone know what this is?
If memory serves, this is a comfort shrug. He likes you!! Here is a great place to read about behaviors and what they mean: http://www.budgieplace.com/behavior.html
You can see if I remember correctly!! LOL