The URL is defaulting to your web browser. To fix, go to Settings > Apps, browse to your web browser (more than likely Chrome) and select it. Scroll down to the section titled "Launch by Default". Click the "Clear Defaults" button.
The URL is defaulting to a undesired podcast app. To fix, go to Settings > Apps, find the undesired podcast app and select it. Scroll down to the section titled "Launch by Default". Click the "Clear Defaults" button.
Contact them! If your preferred podcatcher does not have Subscribe on Android available, contact, tweet, facebook, etc to let them know.