The obvious answer is that Reincarnation indisputably exist in the Zelda universe, and it does not just effect the holders of the triforce, because Malon, Talon, Ingo, Beedle, Tingle, Impa, the Oracles, Mutoh the Carpenter, and possibly a few others I'm forgetting, also reincarnate in other games besides Majora's Mask.
Don't Talon and Ingo only appear in Ocarina of time?.
Their alternate versions (Milk Bar owner and Gorman) appear in Majora's Mask but that"s about it.
Malon, Talon, and Ingo have also appeared in Minish Cap, Four Swords Adventures, Oracle of Seasons, and A Link Between Worlds ( Well, that last one was just Talon and Ingo, no Malon in ALBW )