Although the above are reflux stills in most cases, intended for alcohol, there are many others for water: http://www.jenconsusa.com/10-Water-S...ill-4000X.html and if you look at the dimensions you will see how small these are.
I am not advocating any method, just stating the fact that you can use either, and that there are advantages and disadvantages to both methods (distillation or deionization).
The bottom line is that all commercial developers and fixers are designed to work with tap water. They contain ingredients that prevent particulate matter from forming from hard water. And so, a true test is to mix some developer with tap water and look for the formation of sediment. I know that that is a harsh way to test due to expense if the test fails, but then it does work.
I don't use DW myself for mixing anything but materials for emulsion making. At EK, I did the same. We had tap water to use to test formulas with. And, what I have said goes for both color and B&W.