When cutting weight for fights, I've always drank distilled water the final four days due to its ability to strip the body of minerals and more specifically, salt. I am not sure that RODI works the same way, but I've never looked into it.
When cutting weight during the last 24 hours, you want your body to release as much fluids as possible. Purging the body of salt will enable your body to release more fluids.
I am not familiar with whether DI water has the same water characteristics as distilled. Due to the distillation process, I think it leaves the water really volatile (acidic, aggressively binds with organic and inorganic minerals, maybe some other stuff). It's typically recommended for this reason that you avoid long term distilled water consumption, but again, I'm not aware that DI possesses the same attributes.
Even if it acted the same as distilled, you're typically fine to drink it as supplemental water to your regular water consumption routine.