Reincarnation is what happens to people with the Echo. Whatever the Echo is, it seems to make souls with it able to withstand being unhoused from their bodies. The point of how we kill Ascians is that we merely don't unhouse them from their bodies, it's also that we shatter their souls into non-structured aether. Lower-tier ascians are easier to kill becasue they can't "hold themselves together" enough to leave a non-living body if there isn't another non-living body close by. This is why the Ascian in the Lvl.58 SMN quest leaves once you get DWT. He's afraid that you will kill him and destroy his body and he won't have another body to jump to. In the Lvl 60 quest, Y'mhitra specifically goes someplace remote so that when the Ascians do ambush you, you can kill them and they really will die. Higher-teir ascians don't need a body to exist, so just killing their body and making it too broken for them to use won't kill them. For that a crazy amount of aether is needed to shatter their aether.

It can be assumed that similar things happen to WoL who dies. Only because they aren't breaking any physical laws and acting against Hydalyn, they go back to the lifestrem. Only their spirit doesn't "break up" so the entire thing gets reborn at once. It's theorized that all the people with the Echo are reincarnations of previous Echo-users that were alive in previous Calamities.

The Dorthal seem to take this idea to the extreme. They seem to think "strong souls" leave the lifestream as soon as they die to be reborn as the next child born into the Dorthal tribe. Some people eventually get tired of this never-ending cycle and want to not be reborn. It seems that dying in (or on) whatever it is in the House of the Crooked Coin prevents them from being reborn. If Nhaama is the Xeala analog for Hydaleyn, and whatever is in the House of the Crooked Coin is somehow linked to Hydalyaen's energy, then it seems like dying there would be similar to an Ascian's soul being "shattered" by a blade of light.

As for why the Dorthal think this... I figure that their founder had the Echo or was a WoL and knowing about the reincarnation of people with the Echo, told his people his reincarnation would be back someday. And over the ages that got garbled into applying to everyone in the tribe and reincarnation happening soon after death. It is worth mentioning that the Dorthal belief in being resurrected is treated similarly to the Orinir's belief that they are descended from Azim and the Mol's belief that the Elder Gods tell them what to do. None of the other tribes seem to doubt that it is indeed happening and none of the main characters from outside the Steppes express the opinion that the Dorthal are wrong. So until there's lore that such a thing could not take place, I'm thinking that there's a good possibility it could actually be happening.

Unlike the kami, which we've had lots of lore info on since 5.0, we havn't gotten any new lore about Xaela religious beliefs since we left the Steppe after Naadam. The Kami have been confirmed to be something that exists separate from the Twevle and Hydalyen, so I wouldn't be surprised to find that the Xaela religion is true as well. Or at the very least was based on something that really did happen a long time ago as opposed to being something made up.