The Magic Amulet is like a transportation device that you will use in Red Dragon Island, just in case you get stuck into something. Like you were jailed in the Old Japan because of having no passport. You cannot go out unless you have a Magic Amulet that transports you back to the tree house whenever needed.
How to Get the Magic Amulet
Once you said you wish to go to the Old Japan, the tree house will start shaking, and then after a while will actually start moving. After a couple of seconds, you’ll be in Ol’ Ancient Japan! Exit the tree house. Jack and Annie will give you a Magic Amulet.