Auto enroll on Apple care means you do not have an action to take on your part. You are automatically enrolled in Apple care if you purchase it at the same time as your computer. The box is just for info only. They track your warranty info by your computer's serial number so nothing to keep up with! If in doubt, you can check your product's warranty info here....
https://selfsolve.apple.com/GetWarranty.do
Congrats on the new computer