Kola is not primarily a ritual substance. Across a wide belt of West Africa it is what a host offers a guest, what a suitor brings, what seals an agreement and what is broken at a naming or a burial. There is a proverb behind almost every stage of the exchange, and the Yoruba ritual use is continuous with that rather than separate from it. Presenting obi to an orisha is doing for a spirit what you would do for a person who had come to your house.
That continuity is a large part of why the practice travelled. It required no specialist, no expensive implement and no fixed building, so it survived the crossing in a way that many shrine practices did not. It is thrown today in Cuba, Brazil, Trinidad and the United States, and where kola is hard to come by, coconut is used in its place, cut into four pieces that are read the same way.
What did not travel as one thing is the reading. The conventions for interpreting the fall of the lobes differ between houses, between Nigeria and the Americas, and between Ifa and orisha practice within the same city. They are taught inside a house, to people who have been accepted into it, and they are not the atlas's to set out. Naming that the systems differ is the honest thing to record; publishing one of them as though it were the system would not be.