Even though "tap water" is safe to drink that doesn't mean that it is 100% pure. (It's not distilled water and it runs through pipes which are how clean?) nor does it mean that it doesn't have substances that may adversely affect your wine or other food. Legal rules for tap water are actually pretty loose. That said even though there are rules, how long did that water problem in Flint, Michigan go on before it was discovered?
Bottom Line if you trust your 'no rinse sanitizer' and follow it's mixing and use instructions Why complicate matters by rinsing with tap water that may or may not really even conform to legal standards?
I've switched to StarSan for most of my bottle rinse and prep, that said I do have One Step and just mixed up a batch of it. I stopped using it because I found that it's shelf life after mixing is rather limited. ( Think I remember something like a week or two?) But since I will be doing several wine projects in the next week or so I decided to start using up my bag of 1 Step powder. BUT I also found out that Star San doesn't get along well with our local tap water (Starts out cloudy) so I have to use distilled water to mix Star San.
Go figure. BUT to answer your question, within it's stated limits I would not expect 1 Step to contribute any off tastes or smells. If you don't trust it, don't use it but also I would never rinse with tap water for my wine making equipment or containers.