Pure RO water is not good for fish, at least not 100% which is why we mix it. Fish due depend on those trace minerals in the water and pure water will effect their osmosis, which is a process all living cells have. In pure water they will be under the constant infux of water into their cells which must be pumped back out. To maintain the proper balance, thus requiring more energy then if they were in impure water. Osmosis seeks to balance out the concentration of solutes "stuff" in the water and in the cells.
DI water I am unsure about it is deionized, meaning no charged ions exists in it. It is not pure water though....
BTW your tap water is perfectly fine as is for the vast majority of fish.