Yes, I've done promos like this before with amazon. It says on their terms and conditions page that they'll refund you the price of subscription once you mail in the form. It usually takes a few weeks to get your refund, but you will get it.
Amazon.com: Frederic Fekkai Summer Hair Zero-Humidity Frizz Control: Sephora
Click there ^ and under the price you'll see a box that says "Special offer...". Remember... it's not any $25 dollar purchase, it's any $25 beauty purchase from one retailer.