Nope, they don’t treat the cisterns because the water has been treated at the conditioning plant. Part of the reason for treatment is because holding reservoirs pose a significant risk for contamination.
In my municipality there aren’t enough cisterns that there’s a significant risk of undetected damage, but larger cities, particularly with tall buildings, will have enough that contamination is able to go longer without detection. It’s why major cities treat their water more aggressively.

Salt is poison. It’s also a disinfectant antimicrobial. You also die unless you get a quantity of it.
Ethanol is a disinfectant poison, and so is lye/sodium hydroxide. Having a pretzel and a beer every now and then is also harmless, despite being cooked in disinfectant, topped with disinfectant, and washed down with yet another disinfectant.

You die unless you get enough water, and you die if you get too much.
Foxglove can kill you, or correct dangerous heart conditions.
Apples contain trace amounts of cyanide. Pears have formaldehyde in them because it’s part of natural biological processes. (Your body actually has special processes for handling the formaldehyde it produces. You still shouldn’t drink it, but pears are fine)

The dose makes the poison. That’s not just a phrase meaning that sometimes you can avoid toxicity, it’s quite literal. A poison is a chemical that disrupts normal bodily processes. Every chemical can do that with the correct (incorrect?) concentration.
If you choose to point to a chemical and say it shouldn’t be consumed because there’s a dose that can be harmful, it’s worth remembering that every substance has that limit.

that doesn’t mean chemical build up or other toxicity related illnesses cannot occur

And that’s the type of question you need to ask, not “is it poisonous at some dosage”. You might be shocked to learn that that’s actually part of what we look at when deciding if a chemical is safe to use in some context.

Also, I don’t drink the pool water because it’s a taboo in my culture to drink water that has had people in it. Doesn’t mean it’s unsafe to drink, since getting some in your mouth is inevitable when swimming. It’s treated much more aggressively because “people are in it” and communal things like that are risks for disease spread.
Kinda like why I don’t sterilize my scissors at home, but my barber does. The public health aspect is why they need a license and training that covers sanitation and the basics of skin diseases.
Also, the pool inevitably has pee in it. at a significantly higher concentration than the chlorine in drinking water, as an aside.