Tap water is the least of your worries (and NYC, if that's where you are--has pretty decent tap water quality--if a little on the base side --which isn't great for azalea which likes soil on the acidic side).
You will have disappointment trying to grow satsuki indoors. Sellers mark it as possible indoors. It's a sales gimmick.
I have satsuki and keep them outside all the time. They get tap water out of my backyard hose and have for years. Haven't had an issue, but my tap water is sourced from the Potomac River and a neutral to acidic on the pH side. They're pretty easy outside. Indoors is a different story.
Tropical plant ( primarily ficus and schefflera) are the best for 'indoor' bonsai. They can tolerate the extremely low light levels and desert-like low humidity generated by building HVAC systems) Temperate zone plants, like azalea, can't tolerate those conditions. They don't last long inside as they need higher humidity, light and air circulation. Some also require dormancy, including some Satsuki azalea varieties (there are more than one kind of satsuki, some have heavier winter requirements, while others don't...it's a crap shoot as to which you will wind up buying as most sellers are unaware of the differences.).