The Scions That Did Not Return

[Iscah]

The exarch is alive and conscious when he dies on the first, turning to crystal after the transfer.

You seem to be confusing cause and effect. He's already turning to crystal.

His soul is able to escape that body because the spirit vessel is waiting. We can see that the auracite component – the container for the soul – begins to glow at that moment. If there is any kind of "semblance of a person without the original soul" going on, then it's what remains in the Exarch's body once that soul has departed: something like an Endless perhaps; body and memories.

Souls are a tangible science in this story's universe.