It's only because Sinclair kept his own secret that the Grey Council does not understand that the Triluminary is functionally a tool for identifying human DNA. They have seen it, for so long, as a way of identifying the most important among them, the genetic descendants of Valen, and even the Nine cannot recognize the truth that Valen and Sinclair are one and the same.
So the idea that Minbari souls were being reborn in human bodies is complete nonsense, but it is built on the fact that "our greater souls," the descendants of Valen, were weaker and weaker representatives of human DNA generation after generation. So there were fewer, and they did not seem to match up to the history of his descendants, and they certainly also couldn't make the Triluminary glow as brightly either. But correlation is not causation. This is a narrative of generational decline that has latched onto data it cannot understand and given it meaning that is exactly the opposite of reality.
But the fact that every human they captured triggered the Triluminary? Means it wasn't just Sinclair's DNA. It was, in some generic sense, that the transformation engine of which the Triluminary is a component is equipped with the human and Minbari genomes somewhat completely. If they knew, they might have used it to murder everyone who could make the Triluminary glow, out of genocidal madness, but they couldn't know, and the mistake was already so deeply culturally encoded that it was even more unthinkable than the idea that Minbari souls were transmigrating into humanity.
