Aside from lax Soviet attitudes towards radiation safety, the thing to keep in mind is that there is a difference between working in an limited area of some level of contamination, and living in a larger area with a more dispersed level of contamination. The radioactivity from fission products (the main contaminant from a nuclear reactor accident) declines at an exponential rate. This means that within a few weeks you are talking about a level of contamination that is enough to be a chronic health threat, but not an acute one.

Decontaminating the areas around the reactor (which is large but not as large as a town or a forest) can be done (mostly it is a matter of washing and measuring and rewashing). And you can have ground rules that will keep someone going to the site from likely ingesting any radioactive contamination: don't eat while outside, don't sit on the ground, don't take anything you find from outside the reactor as a souvenir, don't put on makeup, etc.

Radiation workers have their exposures monitored with dosimeters and can be told not to come in again if they hit their weekly, monthly, or annual limits. They are also a non-general audience: they are adults, they are not going to be allowed to do the job while pregnant, and they know their jobs and how to avoid contamination. They are also much more finite in number: a large nuclear power plant might have several hundred people working at it at any given time, on shifts that will end eventually and they will go home (to be replaced by others).

Contrast all of the above to the situation of the town: thousands of people, untrained, much larger area, all ages and genders and maternal situations, living there 24/7, eating and drinking and walking and playing in the dirt, unmonitored, no where else to go but home.

The latter is a real contamination problem: you're going to potentially see upticks in childhood cancers, birth defects, long-term cancer rate increases, etc. The former is not: you can reasonably keep exposures small and in a small population of people you aren't going to see the small statistical upticks in problems, especially if you are being conservative about who is going there (no children, no pregnant mothers — you don't want people whose bodies are growing, because you get more problems with more cell multiplication).

So yeah, you can have a town be evacuated but the plant still active, if you bus people in everyday to work at it, and they live off-site. It's a very different situation between the two.

We might separately ask whether the Soviet monitoring and care was as good as it could have been for those workers; I don't know off-hand. I suspect it was adequate but not perfect ("not great, not horrible," perhaps). But even in an imperfect situation you still would be unlikely to see big effects if the number of people was kept relatively small (compared to a town) and you circulated people through regularly (so their cumulative exposures weren't too high).