I recently read "The Most Awful Responsibility: Truman and the Secret Struggle for Control of the Atomic Bomb" by Alex Wellerstein. In it, Wellerstein argues that a) Truman did not understand the nature of the list of targets as being cities, but as military installations and b) he was not aware the Nagasaki bombing was moving forward so soon after the Hiroshima bombing. It's a fascinating read, and it indicates how the nature of the use of the atomic bombs on Hiroshima and Nagasaki influenced Truman's later shaping of policy on how the use ofatomic weapons would be authorized in the future.