The throne is timeless, but not completely removed from causality. To use the famous analogy by Kyte, think of the Throne as a Wikipedia. At some point, someone makes a page for some hero, and writes down their whole biography. That page now contains the entirety of that hero's life, from start to finish, or multiple starts and finishes if applicable. That's the "timeless" it refers to. In the Universe of Awareness or Observational Space, "history" exist as "events to be observed in sequence", which creates the concept of "time", whereas in the Throne, a Universe of Record or Archival Space, "history" exist as "data that can be randomly (read: non-sequentially) accessed."
However, it still has a history of changes, and at some point anybody (with enough clearance) can edit it, lock it, delete it, etc, and from that point onwards anyone accessing the record will receive the updated version. After a HGW happens and the spirit is returned, an addendum is added to the page. Hence why Amakusa can be a candidate for a Ruler even though hes originally cheated into the class because the events of Apocrypha made the throne add a record of his stint as a Ruler. Unrelatedly, when Ars Nova is used, the page is locked forever (for the observed), but the record, its contents and its history of changes is still there.
This is also how Gil can be "The First Hero" even though there's other, older Heroes recorded. Gil was the first page to be ever written, and then the metaphorical editor went back and added all those guys that came earlier. No matter how many articles you write about things and people that came earlier, Gil's page will forever hold the distinction of "the first article added to Wikipedia".