Diamond discusses this theory in the Prologue, on pages 22-3 in the paperback edition of the book. We should note two things. First, this is not Diamond's theory. Instead, it is a theory that he rejects. Second, it does not claim that the development of irrigation affected the mental development of people in these civilizations. Instead, it says that the development of irrigation made civilization possible because it "required centralized bureaucracies."
The argument, then, is that areas that need irrigation are more likely to develop organized, centralized governments. They are more likely to become "civilized." This is because irrigation projects are are complex and difficult to fund and to coordinate. Therefore, people argue, places that needed to have large-scale irrigation systems also needed to have more organized governments. This forced them to develop more quickly than people in other areas, but this development was political and governmental, not mental.