On the New Stories listing, I've seen the new stories being called A Swarm Cycle Universe Story, A Swarm Cycle Story, and other variations. That leads the reader to believe the Universe's name is A Swarm Cycle or just Swarm Cycle - neither is correct. I vaguely recall seeing other variations of the name.
On any of the story lists, if a story is officially part of a series or universe, you should see, directly above the story description/blurb something like:
A Zane's World - The High School Years Story (3)
This will appear in either green or red text, highlighted in yellow and underlined, it will also be slightly larger size text than the regular story description. This is the official universe/series descriptor, which can be different from the name it appears under in the universe/series lists. This is also a link to the page for that universe/series.
What you should see for Swarm Cycle stories is "A Swarm Cycle Story"
If you just see A Swarm Cycle Universe Story, A Swarm Cycle Story,or other variations in the same font as the rest of the story description, that story may be set in the named universe, but it is not officially in the universe and will not be in the story list on the universe's page.