Reading RSS feeds in native iOS 8
It is apparently not possible to subscribe to a feed unless the page is coded to include that feed as an alternative to viewing the page.

In other words, if I visit (just by way of example) Daily Mac Tips, I can click the Bookmark icon at the bottom of the Safari window, then the @ (Shared Links) tab, then Subscriptions at the bottom, then Add Current Site at the bottom. New stories from the RSS feed on this site will now appear in the Shared Links tab in safari. The fact that Safari knows about the RSS feed for this site is a result of the way the site is coded.

However, there is no way to manually add an RSS feed to this list in iOS. So, from a page like you gave as an example, where there are links to various RSS feeds, the above steps don't work. The site is not coded to let Safari know about the RSS feed, because there are a couple dozen to choose from, and none of them are specific to the page you are viewing.

You can long-tap on an RSS feed link and copy it, then paste it into a third-party app of your choice, but there is no way to subscribe to it in Safari unless the site is set up as described above.

(Regarding it opening the Podcasts app by default, Apple has apparently reassigned handling of feed URLs to the Podcasts app, presumably because they don't have an RSS reader and have removed manual subscriptions from Safari.)