In my opinion, if he is jumping to the floor, that means he is comfy with his new surroundings and wants to explore them. Show him round the house on your shoulder. Walk slowly and let him get the lie of the land. He may want to know where you go when you leave the room. Is he jumping off to the floor to come to you or to look about his new home? Is there a problem with him walking around your house? cats dogs etc? is the problem you parents telling you that he shouldnt be out and about? Why are you sitting him on top of his cage ? why is he not IN his cage if you want him to stay in one place? I recently learned thats its not cruel for a bird to have some cage time. But I KNOW they love to be out with us. Skippah never leaves his perch, NEVER, because its his safe haven. You must try to make his cage his safe haven. Nothing BAD should ever happen near his cage. Never clip or towel or do anything traumatic while he is in his cage. then, when ever he he is worried, he will head for his cage, and thats what you want. Dont make the cage his prison or he will want to get away all the time. When the Professor jumps off his cage to cause mayhem I herd him back to his cage like I was herding sheep, arms out, guiding him. Dont pick him up and put him on his cage. Herd him back to his cage, chatting as you go about "get back on your cage young man"! What do you think you up to? When he has walked( calmly, not paniced while being chased by you) back to his cage, if he wont or cant climb back up, lift him to the top and pat and praise him. Then don't disappear. Let him see your close by and not doing anything too amazing. I will edit this for spelling then add to it. You asked kiddo, so now sit down and do some reading.
Please remember I am not a bird expert and I only know about what has worked (and hasnt worked) for me in the past. If I think I dont know the answer, I wont speak.
Good luck youngen. Im sure if you put some time into it, your bird will come to love life with you for all time.