Chlorine - does it really evaporate?

I'm also a water operator and I've been leaving buckets out to "evaporate" since my Dad taught me many moons ago.
Go right to the source. Ask you water company to send a Consumer Confidence report, something they should mail you each year.
Find out what they add, especially what the free chlorine residule is at the end of the system. If the source is ground water, they may not even add chlorine, or keep a low residule.
My home tap ran about 0.2 free chlorine and I would add that straight to the tank in small amounts with no sign of any effects on fish. For larger water changes I staged in a trash can, mostly for temp adjustment and never got residule by the time the water reached target temp.
Water containing lots of organics, tannins, Fe, Mn etc will consume chlorine residule very quickly.
Warm water gives up its residule much faster.
Vigorous aeration will drive off chlorine residule very quickly.
Fresh GAC will adsorb chlorine to some extent but I'd be leary of trusting it alone.

My local water treatment department's reports don't include what is added to the water, and they wouldn't volunteer the information when I called to ask. I asked them if they added chloramine and was told, "Not right now." I had to figure out for myself that that meant "not this time of year." It's difficult for someone like me who doesn't know what specific questions to ask.

I don't know why they wouldn't tell you, it's not secret. EPA and state regulatory agencies require them to carefully record in detail all aspects of treatment, but especially disinfection and reduction of chlorine byproducts. They are tested often and test results should be availbale. I thought that would be in the CCR.
Lotsa places only use chloramine in the summer, chlorine alone in winter.
It's worth asking questions because you ought to know what they use for oxidation, pH and corrosion control. Those can impact your tanks alot more than a mild chlorine residual. Orthophosphate is a strong algae fertilizer. Some keep pH in the 8s or even 9s for corrosion control/lead & copper.
I'd call the h2o department again and ask for a supervisor. I can see you getting that kind of response from a low level operator. Talk to the chief operator, plant manager, DPW director or whoever can answer your questions.

Thanks for the advice!