When Asimov was writing his robot stories, the technology that people were really interested in wasn't robots, but atomic power. And you can see this in Asimov's stories with the way that he uses "atomic" and "hyperatomic." For instance, the robot's energy system is a "tiny spark of atomic energy" (Runaround.38) and Powell and Donovan build a robot in "Reason" with "atomic flare" tools (Reason.156). So the robots are clearly connected to atomic energy because, in some ways, they're standing in for atomic energy. The characters in the stories worry about robots, whereas people who were reading the stories around the time they were published were worried about atomic power—and weapons.
There are a few other times that Asimov uses "atomic" and "hyperatomic" that might make us think about atomic energy and the atomic bomb. For instance, in "Little Lost Robot," Major-General Kallner is in charge of the Hyperatomic Drive program, which should remind us of Brigadier-General Leslie Groves, the man who was in charge of the Manhattan Project. For another example, US Robots is racing against Consolidated to build a Hyperatomic Drive in "Escape!"—and that might make us think about the US and Germany racing to build an atomic bomb.
But here's one thing to keep in mind: although we often think of atomic energy as dangerous (it can be used in bombs and nuclear energy plants may have problems, like what happened at Fukushima), in the 1940s, a lot of people were a lot more optimistic about atomic power. For instance, check out this picture from the Atomic History Museum of products that are marketed as "atomic" or "nuclear." Atomic energy used to be really cool—people even used to have parties to celebrate atomic tests. So when Asimov uses the word "atomic," we should remember that atomic energy in the 1940s was new and exciting. While it could be used to create weapons, it could also be used to make life better. So in that way, atomic energy really does seem related to the issue of robots: everyone is worried that they'll be dangerous, but they also might just make our lives a bit better.