During at least some point during my tenure as H, I remember doing exactly as Anna describes in the first post. However, over time my stance has changed on this.
What Vance describes makes the most sense. Starting Renown for new a Cliath (that wasn't played as a Cub) is trying to account for some period of time during which that Cliath was a Cub, and during which time they did things fitting of their Auspice. The "Renown for things you did as a Cub" is already built-in. If you earn more than that by the time you RoP, then bonus! Of course, I wouldn't have a problem with anyone wanting to opt-out of the extra if they so chose.