I still don't think the allegory works for growing up, and the only way Jinny can know that it really is important for her to leave is to ignore both common sense and logic (the sky can't fall; no one has ever come back or even sent a message back, which doesn't bode well; there's no reason given for why you have to leave other than "because") and trust solely in tradition. Obey arbitrary rules without question or the sky will LITERALLY fall, kids!

I mean there are definitely adults who would emphatically like pre-teens to fully internalize that lesson before teenagerhood, of various cultures, both faithful and atheist. And it seems like the problem (per the allegory) isn't Jinny going through menarche period, but rather going through menarche on the island - the island is only for children, neither for babies (arriving at toddler-age) nor those going thru puberty.

Like poking at it I think that in fact yeah, the allegory here is literally engaging with the idea that there are some seemingly Arbitrary Rules/Traditions that one must simply follow, as a child, or Terrible Things will happen, because tradition knows better than you and you're too ignorant to know or understand why.

That's a bullshit message that I definitely hate, but if you do assume that's what the author is engaging with, what you describe makes sense, within itself.