Two things about the HBO series kind of intrigued me in how a town situated next to Chernobyl reacted to it exploding.
The first was the obvious one. How long until a mass evacuation is ordered.
The second one might not be so obvious. There's a scene where a charge nurse is discussing with a doctor how many iodine tablets or IV's they have and how it's not going to be anywhere close to enough.
So these two things got me thinking. Obviously after the meltdown it changed the way how nuclear plants all over the world upgraded safety features and whatnot. But did towns all over the world next to these power plants change at all. Where there mass exodus of their citizens to "safer" towns farther away? Did hospitals and emergency services change anything?
How did Chernobyl change these towns?
My knowledge on the public response to the Chernobyl incident isn't thorough enough to sufficiently answer your second question, but I can answer your first (which is a more policy-oriented question better suited for r/nuclear or r/nuclearpower probably).
Nuclear Energy incidents follow the International Nuclear Event Scale, a logarithmic scale where each level is ten times more severe, such as the moment magnitude scale used for earthquakes. The difference is that for nuclear accidents, this scale is highly subjective, rather than objective like with earthquakes.
As a result, the order to evacuate is a decision made by the regulators overseeing the response to the accident in the country it occurs. There is no real standardized practice for when to evacuate, and this has caused serious social, economic, and health problems actually. Scientific studies have revealed that 3/4 of the Chernobyl evacuation was unnecessary, along with the entirety of the Fukushima Daiichi evacuation.
Much of the scientific debate over when to evacuate goes all the way back to the debate over the BEIR report and the establishment of the Linear Non-Threshold model of radiation, which utilized data from Hiroshima and Nagasaki survivors, tests in animals, and from other early radiation exposure incidents to establish that there was a linear dose-response relationship between radiation and cancer risk. The problem is that the data only supports this relationship for high doses, above 200 milliSieverts (mSv). Since 1996, this has been increasingly disputed by radiation scientists, and there's possibly some evidence to suggest that the LNT model was pushed for political, not scientific, reasons. The problem is that there is currently no real alternative. Radiation Hormesis (which suggests low-dose radiation triggers the body's immune response and reduces cancer risk) is a new theory but has yet to receive widespread scientific acceptance and has been rejected by the National Academy of Sciences twice, most recently in the BEIR VII report. But neither LNT, Linear with Threshold, or Hormetic models have enough data to support any of them at doses under about 100 to 200 mSv.
As a result, the decision to evacuate is largely based on regulatory limits on radiation exposure rather than actual health consequences. These limits vary from country to country, but are typically set at about 1 mSv per annum for the public (see 10 CFR 20.1301) without a permit to exceed this limit. There are also social and political factors that go into ordering an evacuation because nuclear energy has become so heavily politicized that the decision not to evacuate would have massive repercussions. Only a couple countries - namely Switzerland's ENSI regulatory body - have reformed their system so that evacuation is now considered an absolute last resort, and should be very limited in nature. But this is not standard practice worldwide, and the decision by and large remains in the hands of political bodies or regulatory commissions.
I hope that helps.