Sinclair used the Triluminary device (that ornate contraption of stacked crystal & metal) to alter his form from Human to Minbari, much as Delenn used the same device 1000 years later to change from a Minbari to a Minbari/Human hybrid. It is never said where Sinclair got the device, but there are three theories:
1.) It was given to Sinclair by Delenn in 2260, who got it from the Grey Council, who had been keeping it from when it was found with Valen in 1260. That means that the machine was never created and exists within a closed loop of time. The paradox gives me a headache, so I favor one of the other two theories.
2.) It was given to Sinclair by Kosh and the Vorlons in 1260.
3.) It was given to Sinclair by Zathras, either in 2260 or 1260, who had brought it from the archives of the Great Machine on Epsilon III (which contain Lorien knows what else), and the device's true origins remain a mystery.
As for how Minbari souls became reborn in humans, the metaphysics are very fuzzy. We know that the Grey Council made that pronouncement becase they detected Valen's soul within Sinclair, but they did not know that Valen & Sinclair were the same man. We also know that the Minbari consider the collective souls of their race to be like a liquid in a container that maintains a fixed volume. I would imagine that they consider the collective soul of Humanity to be the same. By becoming Minbari, my conjecture is that Sinclair/Valen created a link between the two, and the two liquids began to intermingle. It is revealed in the novel To Dream in the City of Sorrows by Jeanne cavelos that Sinclair's fiancee, Catherine Sakai, fell through the time rift in Sector 14 and that was one of the reasons Sinclair was so eager to go on a one-way trip to the past. It is revealed in the DC Comics miniseries In Valen's Name that Sinclair/Valen eventually found Sakai in the past, and I would suspect that he used the Triluminary to transform her as well. We know that Delenn and many other Minbari are descendants of Valen, presumably by the transformed Sakai. It is then really a matter of perspective as to the question of Human and Minbari souls: Unaware of their own Human ancestry, are the Minbari simply seeing elements of Human souls that are present in themselves because of Valen's lineage and mistakenly assuming that they were originally Minbari?
As for Legend of the Rangers, I admit it was rough in places, but I thought it had great potential. I liked Captain Martell's devastatingly clever methods of escaping the Hand's forces; Terk, Na'Feel, and the Minbari telepath whose name escapes me were fun characters; and Sara's Zero-G VR Gunnery station was seriously cool. The biggest flaw I found was the danger of the Hand coming across as tired retreads of the Shadows, and if it goes to series I would hope they play up their Lovecraftian Elder God aspects.