If I understand correctly, to use the Uber One credit you need Uber to charge you, but you need the full amount on your card, not from your cash or credit balances?
Yes, correct. It says so clearly under How it works in the screenshot provided. You must use the Amex Plat card as the payment for the Uber one membership and you get a statement credit against it. It also says that you must toggle off Uber cash when signing up so that it won't use that as payment.