Hi there and welcome to TB!
It's great to know you've decided to adopt little Pichi! I bet he's just adorable and it's a good sign that he's eating and playing! However, I think you're moving a little too fast for your little friend.
It's usually recommended you give a new bird 2 weeks to settle in. Even though you're excited, it's still the best for him so he can settle into his new home.
After two weeks, you can start taming him. He probably let you stroke him as he was indeed terrified, he's in a new place and budgies can't help but be submissive for the first few days.
Start by sitting by his cage and just talking to him or reading during the two weeks to get him used to you. Then, after the two weeks is finished, you rest your hand in the cage lightly for a few minutes a few times a day until he's comfortable, then you can put your hand closer to him a few minutes a day, and finally you can start "step up" commands. During this time, you can offer him seed in your hand and see if he eats it, this is good for building trust.
If you do it like this, he will probably adjust to you much easier
Hope this helps! Best of luck with little Pichi and we'd love to see pictures when you get a chance