The lore book pretty frequently conflicts with information offered in-game on multiple subjects tbh.
If this were the case, M’zhet Tia would not have been able to continuously challenge the Nunh multiple times or rejoin the tribe without becoming Nunh first, and his father (a former Nunh) is cited to have left after the tribe’s numbers dwindled— he wasn’t exiled.
That, and we’d have a bunch of Nunhs in the wild because they’re all trying to start their own tribe.
My understanding is that a Tia’s options are to win against the Nunh or remain a Tia in the tribe. If they want to become a Nunh but cannot beat the current one, they leave to form their own tribe, but this is rarely successful.