... delete it from his account, and registered my card to my account on April 1, and saw the $15 show up under a new "Credits' section.... 1. Delete the eligible card as a payment method on the Uber account(s) with the eligible card on file that you do not wish to receive the benefit.* 2. Add the eligible card as a payment method on the Uber account you wish to receive the benefit. If the eligible card is already on this account, skip this step. 3. Complete steps 1 and 2 by 12:00am EST on the 1st day of the applicable month that you want the Amex credits to apply to the applicable account.
It sounds as if you needed to link the card to your account on the 31st. Have you looked to see if there is an April credit on your son's account?