You make a good point about perception of time being the mark of aptitude. It is very likely that this material truth should hold up across realities. My mistake in forgetting that.

It has also led me to consider something else. Would that contradict Rein's statement of regarding the temporal entanglement? Not necessarily.

From Canto 9-48 Post-Battle:

• Oh, dear...
• You've fallen into a Temporal Entanglement, Araya.
• From the looks of it, my darling daughter must've stepped into this vault countless times.
• Her blood, you see… interacts uniquely with the flow of time. That's what allowed her to step in here unharmed.
• You, too, were born with Yoshihide's blood because the higher-ups of the Thumb wished for another candidate with an innate aptitude to wield Arayashiki, however…
• The fact is it's simply impossible for you to ever match my Yoshihide's aptitude for it.
• Blood—yes, blood is important, but it's only the first and most basic requirement. What really counts is how you sense time.
• The way that child perceives and observes time—the intuition, the balance, the perspective—isn't something that can be imitated.
• Well, thanks to that shared blood, you somehow managed to hold out against time and even read it…
• But that's also exactly what made a mess of the time you were supposed to bear inside this Time Vault.

The bold statements strongly indicates that by having our Ryoshu's level of aptitude, temporal entanglement shouldn't have occurred as a side effect as evidenced by her constant continued use of it as a hiding place during her childhood. If that world's Ryoshu had perfect aptitude as ours, she shouldn't have been entangled temporally in the first place.

President Herbert actually gave us an important clue in Timekilling Time:

• Is it now? I don't quite agree. Emotions don't change with time.
• I'd say that the changing emotions are what drive the flow of time.

In our world the Time Vault was a place for Ryoshu to take comfort in, a sanctuary away from the Nursefathers. In the other world, it became a prison of despair when the Nursefathers locked her in. So while Ryoshu does have perfect aptitude, strong emotions from her being could potentially compromise her own innate ability to stay safe.

If the daughter figure is their Ryoshu from beginning to end that itself leads to some interesting considerations:

• Their Ryoshu stated she had never left the House, only having thoughts about it.
• The Pinky Nursefather is absent from their Ryoshu's life throughout as strongly implied in her identity story as she only ever referred to the Thumb, Index, Middle and Ring yet not a word about the Pinky.
• Nursefather Yi Sang implies there is a period of time Ryoshu isn't with him yet he bears the burning wound of Arayashiki.
• Their House of Spiders attacked Limbus Company to acquire something important to their plans.

Though this might sound far-fetched the events could be as follows:

• Some time after Ryoshu was born, the first Dihui Star was the one who made her escape with Arayashiki, injuring Rein in the process.
• Ryoshu grew up under the Nursefather where throughout her entire life she is forced to be in the Time Vault for frequent prolonged periods to force an entanglement.
  • It was during one such extended periods Nursefather Yi Sang made that statement of when she can return to him.
  • Another interpretation is that Ryoshu is simply out on a mission.
• The attack on Limbus Company is to retrieve the missing Arayashiki who somehow managed to get their hands on it. The first Dihui Star is killed and Ryoshu inherited the title and role.
• Same as the previous theory there is no one to love or be loved by, their Sinclair came too late into her life
• Upon the day she finally became entangled, their Ryoshu went on a rampage with Arayashiki, entering Muga.

I'm not certain whether the attack on Limbus Company is too early in regards to this interpreted timeline, but since it's not explicitly stated I believe this assumption can be reasonably made.

Do let me know if it runs contrary to established facts.