Tap water has all kinds of crap in it that you don't want, chlorine, fluoride, metals (iron, copper, etc), all the type of stuff that can kill your corals.
I say CAN, not "definitely will." RODI is one of those things that helps you be successful and eliminates a lot of head scratching when things go wrong, from the uncertainty of what chemicals were in your source water.
If things are fine so far, I'd proceed with adding your corals, and continue to do your weekly water changes. If you want to get rid of the tap water faster, do maybe 20-30% per week for the next 4-6 weeks, that should get so much of it that the rest is negligable.