The accounts from people there (such as those found in Hersey's Hiroshima) show people who assumed initially that a bomb had been dropped on their house specifically, and only gradually realized that the entire city was affected. They did not know it was an atomic bomb, and there was considerable confusion, as you would expect from people who experienced it from the ground.

The Japanese government acknowledged on August 8th that a "new-type of bomb" some days after the fact, but the Hiroshima inhabitants would have had a hard time learning that, given the state of communication with their city. It was not until August 9th that the Japanese government acknowledged that it was an atomic bomb.

Radiation sickness was not really acknowledged/observed until after this point, and it was the physicians in hospitals who figured that out. Other people just noticed that people did OK and then did poorly and then briefly seemed OK and then they died.

When we look back at events like this, we tend to see them in the aggregate — "oh, people died of X, this much of the city was destroyed, etc." But you have to remember that the people involved on the ground only could see it through a very narrow pin-hole of perspective: their own experiences. And it was very hard to reconcile their experiences with what they knew about in the history of warfare up until that point, so it is very understandable that they didn't make much sense of it.

John Hersey's Hiroshima (1946) is a classic read on the experiences of people in the city after the bombing — it is heavily recommended.