The only real reason I know of for letting water sit is to allow for pH to equalize. Some salt manufacturers may balance the ingredients in their salt mix to produce a relatively high pH upon mixing. The pH will eventually trend down (assuming your home is like most and is rich in CO2) and will likely settle around your tank's pH. It just takes time for CO2 to dissolve in the new water and for the carbonate/bicarbonate/carbonic acid balance to shift into equilibrium.
Having said that, letting water sit for this reason isn't even necessary. At most, in the above case your tank's pH might increase a little bit, but that's about it. Sodium carbonate and calcium hydroxide additives also increase pH by a small amount with no ill effects (provided they are not overdosed). I don't even match the temperature of my water changes (although I do keep my water inside, so at most, it's only off by 10*F from tank temperature). As long as salinity matches and the water is clear, I use it regardless of how long it's been mixing.