In this instance, "jump" is a verb. Douglas, the protagonist, is lying in bed picturing all of the fun things he's going to do in the summer. He is picturing his hands grasping fruit from different trees quickly, almost in a frenzy, so he uses the word "jump".
He uses the simple tense because he is narrating the image as if he is an outside viewer watching a scene in real time. But you are correct, the meaning would be the same if he had said his hands were "jumping" everywhere and he was "plucking" fruit.
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