This is such an odd little turn of phrase.

I live in Birmingham, AL and have only heard this in the past five years or so. I've only observed it with African-American co-workers, but I don't think that makes it an exclusively African-American "thing." I went to public schools here in Alabama and I've never heard an educator use it.

Although it may make sense that it derived from "on the morrow" I really don't think that most of the people I hear using it are trying to say that.