Stripe are obviously taking the risk of the volatility so will probably want to keep the bitcoin float that they hold fairly small. They also need to keep a reasonable margin on these transactions and watch for people who don't complete transactions unless the price moves in their favour (after the price has been quoted).
I assume refunds are of bitcoin to the agreed dollar value not the same number of bitcoins as was spent, otherwise there would be risks there too.
Edit: Found this in other story: https://news.ycombinator.com/item?id=7481219 (http://recode.net/2014/03/27/stripe-merchants-will-soon-be-a...)
Payments will arrive in their bank accounts in seven days or fewer. Neither Stripe nor its customers will hold onto the bitcoin, meaning the businesses that accept bitcoin will not be subject to the volatility of its price. Collison said his company is working with a variety of undisclosed partners to exchange the bitcoin into local currency in near real time.