No, he bit you because he was scared. You grabbed him thinking to help, but it scared him even more, but now that he has calmed down and feels safe again he is alright, and he is going to remember and think about this, it is all just a step in his learning to trust you and since you did not hurt him and put him in his safe place he is that much closer to being able to trust you. Except for getting in a little bit of a rush by letting him out from the top of the cage you did well. Everything is fine. A parrotlets very first reaction when scared is to get away if this doesn't work then his next action is to try and defend itself by biting. They are very small and fragile and do not have many options. Grabbing him even though you did not hurt him is very similar to what it feels like to be grabbed by the mouth of a predator, so what would you have done if you had been him? Try to look at things from his perspective. Try to think how big and scary and dangerous the world would be if you were his size and almost everyone and everything were that much bigger than you and you know that some of them just want to eat you.
Parrotlets are very much like larger parrots and they are very protective of their territory so when someone lands on their cage which is their safe place and the only place that they can claim as theirs they are going to defend that place from the intruder.
If he is not yet stepping up onto your hand to get a treat at the door of his cage, then he does not trust you yet. Do not chase them around if they do not step up as it just scares them.
Now if they are coming to the door of the cage to get a treat from you and are staying there to eat it calmly it is time to move on to the next step. You can try holding the treat in one hand and place the other one at the cage door for them to step up on and hold the treat so that they need to stretch a little bit in order to reach the treat. It should not take very long and they will be stepping up on your hand all on their own. Once they are doing this then they will also step up for you in other places as well.
It would be great if you could post some pictures of them her so that we could see them, we love pictures.
Now is also a good time to start teaching them to target and so I am going to post a link here for you to read, it will explain the basics of target training as well as another way of teaching them to step up for you. Here is the link :
viewtopic.php?f=11&t=227 Please let me know if I can help you more.