I always wondered if there ever was a Tentei. I know the guide mentions it but I'm not sure if that can be taken as canon.If there's still a Tentei, it's possible the mirror is with him and/or at the cliff temple/Chi You Men base.
But yeah the ending makes next to no sense so it's almost pointless trying to get a grasp of it.
Suzuki has always mentioned four leaders of the CYM and nothing else. If anything it always seemed that the northern leader, Xuan Di, was the de facto leader if there ever was one.
That being said it does make sense from an organizational standpoint to have a big boss ruling over the CYM, unless we are to believe they are a 4 person democracy. Alas, Shenmue 3 missed the opportunity to delve deeper into the CYM lore giving us some clues to work with.