I'm a bit surprised this was left ambiguous in the text, as it would seem to have a pretty big impact on status jockeying. From the Princess's perspective, increasing status first means a smoother transition from 3 -> 2 -> 1 Permissions (for Ace / 1st Wing / below), but for the rest of the cadre, it makes earning that Ace permission much harder - not only do you need to excel yourself, but you also need to either make sure the Princess isn't right behind you, or bait it into breaking one of its rules.
(That said, perhaps a good Girl should know to stay out of the spotlight when in the presence of a star, rather than struggling against the current - more total Permissions across the cadre means more/stronger assets and more success in the war, which is what really matters, right?)