It originated in the Niger River basin. Its spread into the relevant parts of W. Africa very likely came later. How much later is up to debate. Again, I disagree with Jared about the commercial prospects of rice when far more convenient Roman N. Africa was already a net exporter of wheat and other grains.
The rice was first harvested 3,000-2,000 years ago and spread across the region. As I already said before, if by the off chance it didn't spread to Senegal, I'll just make it so that it spread slightly faster. And the point of harvesting the rice wasn't to feed the Empire, it was to simply add diversity to the Romans' available food. It's a different species of rice that the Romans had never tasted before.
And not to sound snarky (honestly) but I was directly asking Grey Wolf on his opinion of it. I feel like I should add a poll on the subject.