SpiderOak uses Stripe, a respected payment processor. Stripe provides us with a JavaScript widget which we place on the billing page. It communicates your credit card information directly to Stripe. Using it, we never see your credit card number, not even momentarily during processing. Just as we do not know your password or what you are backing up, neither do we know your credit card number.
To provide you with this security, the widget needs to load, so be sure to allow JavaScript from stripe.com and stripecdn.com in your browser when viewing your billing page.