It doesn't necessarily have to be a credit card as i've used my visa debit in the past, but yes a deposit is needed of some sort to secure the booking.
You need to give them your credit/debit card number but no money is taken at all, unless you are a no show, and haven't cancelled within 48 hours of the ressie - u can even pay in cash on the night!
You just need your card when you actually book your ADR for Fantasmic.
Kx