When you download the paid version, it will not delete the free, ad-based version from your mobile device - make sure you are opening the ad-free version of the app. The paid version is the Dictionary.com logo and icon but it is surrounded by a silver frame.
If you do not have an app installed on your device at all, then simply return to your app store and download Dictionary Pro again. Just be sure you are using the same user account you initially used to make your purchase.