Normally it will open an RSS reader app, if you have one installed. I've never heard of it opening a podcast app. Though sometimes podcasts are distributed using RSS, so the app may have registered itself as an RSS reader.
You can also hold down the button to copy the link, then open your RSS Feeder to add it manually (usually a + button somewhere in the feed list.
If you are using the Feedly website, it also offers the ability to manually add RSS links.
Most modern RSS reader apps will sync with Feedly, so it is perfectly possible to start with Feedly and get a dedicated RSS app later, if you want a different reading experience and/or features.
Reeder 2 is my current favorite RSS reader. It's available on iOS and the Mac, in their respective App Stores. There are dozens of good to great RSS apps, so it's mostly a mater of taste and feature sets. Reeder 2 is a middle ground reader, reasonably simple to use with a good set of features. I mostly like it's interface, easy to use good looking. Experts may feel the need for more flexibility and power.