I grew up in Atlanta suburbs and I first heard "On tomorrow" in middle school, from an English teacher. I argued with her until I turned blue, but could not convince her that it was flat wrong. I continued to hear it from time to time, mostly in school from educated southern African-Americans, and as the phenomenon continued, I started hearing other people also using the term. As far as I can tell, it's an invasion of the language that is abhorrent, and as Catrice said, I just want it to stop!
I don't think it is something that is only taught to "Black people only". but I think it is mostly those who are picking it up from the educated black educators.