Kiyoshi Tanimoto, pastor of the Hiroshima Methodist Church, paused at the door of a rich man's house in Koi, the city's western suburb, and prepared to unload a handcart full of things he had evacuated from town in fear of the massive B29 raid which everyone expected Hiroshima to suffer. (1.1)
When the book opens, we learn that the residents of the city had been living in pretty much constant fear of attack. Because of that anxiety, Mr. Tanimoto and others had been moving personal belongings out of the city center to safe locations in the 'burbs.
Of all the important cities of Japan, only two, Kyoto and Hiroshima, had not been visited in strength by B-san, or Mr. B, as the Japanese, with a mixture of respect and unhappy familiarity, called the B-29; and Mr. Tanimoto, like all his neighbors and friends, was almost sick with anxiety. (1.2)
Hiroshima residents were especially anxious since they were one of the only major Japanese cities that hadn't sustained a major hit in World War II up to that point. It seems like the worst most people were expecting were B-29 attacks.
The frequency of the warnings and the continued abstinence of Mr. B with respect to Hiroshima had made its citizens jittery; a rumor was going around that the Americans were saving something special for the city. (1.2)
As if B-29 attacks weren't enough reason to be afraid, it seems that the fact there hadn't been one of those attacks yet made some people worried that something even worse or extra "special" was on its way… and, of course, these people were right.
He moved nervously and fast, but with a restraint which suggested that he was a cautious, thoughtful man. He showed, indeed, just those qualities in the uneasy days before the bomb fell. (1.3)
Hersey's description of Mr. Tanimoto paints a picture of a nervous, careful person overwhelmed by the "uneasy days" that had preceded that one.
Mr. Tanimoto cooked his own breakfast. He felt awfully tired. The effort of moving the piano the day before, a sleepless night, weeks of worry and unbalanced diet, the cares of his parish—all combined to make him feel hardly adequate to the new day's work. There was another thing, too: Mr. Tanimoto had studied theology at Emory College, in Atlanta, Georgia; he had graduated in 1940; he spoke excellent English; he dressed in American clothes; he had corresponded with many American friends right up to the time the war began; and among a people obsessed with a fear of being spied upon—perhaps almost obsessed himself—he found himself growing increasingly uneasy. (1.4)
With the anxious atmosphere of that time came a fair bit of paranoia, it seems. Not that we can blame anyone for being paranoid. Aside from fearing imminent attack, the people of Hiroshima were apparently super-tweaky about the prospect of being spied upon. Hersey makes a few references to this vein of paranoia.
Dr. Fujii hardly had time to think that he was dying before he realized that he was alive, squeezed tightly by two long timbers in a V across his chest, like a morsel suspended between two huge chopsticks—held upright so that he could not move, with his head miraculously above water and his torso and legs in it. (1.18)
After the blast, Dr. Fujii was clearly so confused and scrambled up by events that he thought he was dying—but that fear had barely gotten a foothold before he realized his immediate problem was being trapped—alive, but trapped.
Then, for a few seconds or minutes, he went out of his mind. (1.22)
This is Hersey's description of Father Kleinsorge's reaction after the blast. Although Hersey doesn't mention fear per se, it seems reasonable to assume that going out of one's mind in response to trauma might have been his mind's protective response to fear. As a result of the episode, his memories from right after the event get a bit spotty.
She was paralyzed by fear, fixed still in her chair for a long moment (the plant was 1,600 yards from the center). (1.29)
This is Miss Sasaki, who had just sat down to get to work when the bomb was dropped. She had enough time to react (or rather, not react) to the flash with paralyzing fear.
Mr. Tanimoto scarcely answered. He had thought of his wife and baby, his church, his home, his parishioners, all of them down in that awful murk. Once more he began to run in fear—toward the city. (2.3)
Whereas you might expect fear to inspire people to get further away from Hiroshima, this wasn't the case with Mr. Tanimoto. Instead of running away or being paralyzed, his fear mobilized him into a sprint towards the city.
Then a thought which came to him—that soon the tide would be running in through the estuaries and his head would be submerged—inspired him to fearful activity; he wriggled and turned and exerted what strength he could (though his left arm, because of the pain in his shoulder, was useless), and before long he had freed himself from the vise. (2.14)
Like Mr. Tanimoto in his sprint toward the city, Dr. Fujii ended up finding his fear motivating, using it to find the strength to escape from his sticky (or at least stuck) position.