We recently had some craftsmen here who created a door between the garage in the basement and the rest of the house. There was a lot of dust, and now in hindsight, I've started to worry if there might have been asbestos in the wall they removed. For someone like me who is not knowledgeable about this, it looks like regular concrete, I think. But the house is from the 60s, and we have asbestos in the floor adhesive in another room in the basement. Could there be asbestos mixed in with the concrete or something else similar? For plaster and similar materials that I've read are more common, you wouldn't use it for an entire wall, right? Or am I worrying unnecessarily?
Yes, you're worrying unnecessarily. As far as I know, it has never been used in concrete. Even in plaster, it is very uncommon. It is more in and near surface layers, like tile adhesive, certain types of glue, etc.
What might be present specifically on garage and boiler room walls are asbestos cement panels on the outside of the concrete. This is for fire safety reasons. But you can tell if there are panels.