It doesn’t matter if it physically happens, just that people believe it. If a holy man dies and a his followers comes across a tiger that they believe to be his reincarnation they may revere it. Not necessarily how this commonly works, but it’s in the realm of possibility.
I’m just trying to rework some of the existing mechanics like Tiger training into a new form in order to preserve them. Various Gurus and ideas about reincarnation are present across India so all I’m saying is it is thematically plausible.
Gurus should have some kind of special ability to prevent them from being another bland, mostly useless healer. Maybe instead of “reincarnation” it could follow the Sikh tradition and allow a new Guru to spawn each time one is killed up to 9 times.