How do Sundered Ascians work? Or Alternatively: Is Reincarnation possible or not?

[KageTokage]

That first short story about Emet Selch states that new souls are just spontaneously formed within life born through natural means, but at the same time makes no mention of reincarnation.

It could just be that they left out that bit, but it also makes me wonder if maybe something changed about the cycle in the wake of the Final Days and/or the Sundering because if reincarnation and generation of souls co-exist, what would determine which occurs whenever new life is born?

The pro-Zodiark crowd intended to sacrifice new souls to bring back those lost in the Final Days, but I'm curious as to how they were going to go about doing that if they potentially had to worry about the reincarnated souls of those who were lost getting caught up in the process.