Well the souls have to go somewhere.¯\_(ツ)_/¯
This is an interesting point. In real life, we're still arguing if we even have a soul (as in a spirit; not sure if anyone believes soul and conscious is interchangeable). In Naruto, that's not up for debate, because they definitely have souls. I suppose if in real life we discovered that souls lingers around after death, that it would fall within our definition of an afterlife, if not pave a way for its classification as such. I'm sure there would be many arguments based on technicalities.
Even if there's currently mythologies and philosophies that doesn't define it as such, it would be more open to universal interpretation once souls, and lingering souls, are established as fact.
......
As for when the souls moves on, unless we start getting into Kishi's inspirations and use that as a basis for deciding this (though, that wouldn't be 100% reliable; not that anything we ever say will), we don't know because the soul could become nonexistent after it moves on. Then we'd start getting into questions such as "Did the soul pop into existence much the same it vanished from existence?"
If it can exist in a state independent of the physical body, it wouldn't be too far-fetched to believe there's a life before birth, in Naruto of course (just letting you know I'm still on track lol). This brings us to the reincarnations, it wasn't Ashura's and Indra's soul, but their chakra. They chose their host, ergo Naruto and Sasuke were already conceived, and I presume possessed a soul. Orochimaru inhabited a body while the soul is still inside its host, and Minato have already shown that it's possible for the soul and chakra to exist as two separate entities.
I wonder, then, how come they didn't choose to reincarnate as themselves. I don't see any moral concept holding
Indra back from doing so, if he was like Madara, it's reasonable to me that he'd enter the baby's body and be fully revived.
Either whatever abstract means they used to transmigrate their chakra wasn't accessible to the soul, or their souls ceased to exist.
This was just to inspire thought, but I guess we may never
truly know where it goes after it "moves on".
Edit: I suppose wandering chakra that seems to embody a conscious/the consciousness of its physical experience would still qualify as an after life, albeit not a wandering soul.
