Iroh’s physical body passed away, but the Spirit World isn’t a catch-all afterlife. The crew compared him to the Painted Lady, who had also started out as a human — the idea is that special people who are imbued with spiritual energy or have cultivated a spiritual connection can transfer their personality into the Spirit World and embody some energy there (which, I’m guessing, doesn’t really impact on whatever reincarnation thing would have normally taken place). Over time, this energy becomes more and more spirit-like as the individual has been without a body for longer, which is why the Painted Lady is more ghostlike than Iroh, but it always retains the underlying personality. (I’d bet money that Jinora ends up taking this path later on in life… and it might explain why past Avatars like Kuruk seem to be able to appear in the Spirit World and affect stuff there, too)