Considering Einsteinian physics, where do they get the assumption that civilizations expand at the speed of light, eventually zipping around so fast that they arrive before their radio signals?
Even if you could travel at the speed of light (you most likely can’t) that doesn’t mean you instantaneously land somewhere, establish a colony and just move on to the next one at the speed of light.
Radio may be a short lived technology with all the smart kids figuring out how to use something like quantum entanglement instead.