I use a hose in the back yard, and I swear it takes a swimming pool worth of water to wash 200 lbs of sand. I finish each barrel with a dose of Prime, which removes chlorine.
The waste water from ro/di contains a concentration of all the minerals and stuff the filter is removing, so it's probably a little worse than tapwater, though some of the stuff may be bound in the filter.
When you install the sand, lay your worst rock down to be buried, then sand, then the rest of the rock using the buried rock as foundation, and interlock the pieces so there's no wobble or shift. Put down a glass or ceramic mixing bowl on the new sandbed before you add water, and pour your water into that to avoid kicking up the remaining dust (which can take days to clear). Alternatively, spread out a garbage bag to cover rock and sand before you add water: it will float as the level rises, but it will also prevent sand kickup.