So the African American spiritualists & Charles D. Tillman got it wrong when they wrote the song: OLD-TIME RELIGION!

I wouldn't make any assumptions about that, although it would be an interesting question to explore. I know that African Americans did contribute to the musical culture that spawned what is now known as "old timey", but while African American spirituals came essentially from African Americans, old timey music came from European Americans as well as African Americans. So there may be some differences in word usage. Also I don't know if African Americans used the term "old timey" to describe that kind of music (prior to the Carolina Chocolate Drops using it), or if the term is/was used only by European Americans. Unfortunately, in the part of Appalachia where I have lived, there weren't very many African Americans, so I have no direct experience myself.