It happens that in 1986 I participated in the cleanup after the Chernobyl catastrophe. I worked as a radiation measurement specialist 20 m below that blasted 4th reactor. I worked at the station for the whole July. It was the worst time, for the radioactive dust levels increased till the finishing of the Sarcophagus.
As we had only masks as protection (but they were really good... when we had them), I learned that people can easily feel the radiation. A radioactive dust particle, sitting on your skin, creates the same feeling which you all know from the sun burn. Only the feeling is concentrated in a point. So, people do not need extra methods to detect half of the problem - the radioactive dust.
The negative side of that skin detection is that you don't feel the burn at once, when you feel it, you are already burnt. And when you feel one particle, probably you had got much more, but you don't feel them YET. Or they are inside you and you won't feel them at all. You must: 1. not allow them to get inside and 2. remove particles from the skin as early as it is possible. The solutions are: wear respirator mask everywhere except wet cleaned closed rooms, cover the skin everywhere, especially in connections between clothes' elements, showering after a walk, washing exposed parts skin even during the walk or work outside. And better don't go out when it is dry and the wind blows. And the time after rain is the least dangerous.
And this way will really work - I worked in the very epicenter, and even didn't follow the rules fully (the needed services were extremely badly organized), but I do live and have healthy children. But I was there only 35 days on the station and 35 days in the town. And your people live there. But they will use not so dangerous territories for living. I think, it will well compensate the longer time.
Notice, there are two kinds of radioactivity you should think about: gamma rays and beta+alpha rays. Gamma rays are much less destructing. But you cannot stop them by clothes. Alpha and beta are much more destructing, but they could be stopped even by air and easily - by clothes. As a result there are two sources of radioactivity. The radioactive dust - you are getting a particle on your skin or in your inside and it is killing you by all three kinds of rays, and the background radiation level from all surrounding, that consists of gamma rays only. If you had got only one radioactive dust particle inside, you don't need anything else. It will sit in you and kill your cells around. And sooner o later, some of your cells around it mutates - and the cancer comes. So, your task is not to allow a single radioactive particle to be on or in you for a long time.
As for gamma-ray background radiation, in our reality the levels that can be felt by organisms are deadly for humans. Of course, your people can find some plant or animal that is very sensible to radiation. Young animal or sprouts are more sensitive. Only by inventing some animal/plant and using a very young form you could compensate our very bad radioactive sensitivity. (look page N.5 here)
As for detection by radioluminescence, it also doesn't work until radiation level is already too high for humans. Only if a luminescent material was put directly to the eye, and the detection was done at night, then separate sparks while a particle passes through would be noticed.
But if the source is an old reactor, then the main danger will be the dust.
There will be another problem. Radiation does not change in a monotonic way - here it is OK, a kilometer further worse, further - even worse, and on that hill the worst... No. You have a clean place here, extremely dirty place around the corner, absolutely clean room nearly because windows were closed, terribly dirty door of this very room, and so on. The fact that you passed the area and remained clean doesn't mean you won't get very dirty the next time. It can happen if you take a slightly different path. Your protagonists should evaluate, mark and remember exact paths, not the areas. And they will need to recheck their paths often enough, for the wind is moving the dust.
It is funny that such society should create a special etiquette. One of the most impolite things you can do there is to raise the dust.
Smokers there could be only among some self-killing fanatics. Smoking worsen the output of dust particles from our lungs. But those people from the tale could invent some medicine to improve such output. They could wash their noses by salty water several times a day.
After some time I got bad feeling about your people - where they will get the clean water? The food can be planted under glass roofs in clean rooms, but I can't think out the source of water for them.