I am going to say it is bull shit that he did not give any decision until after the first two bombs were used. That is the writer skewing one bit of information and pretending nothing else could have happened before it. That plans were already in place for the use before he became President makes sense, but he would still be involved upon hearing the plans to veto them, change them, request delays, etc or to authorize the plans to go ahead.
The idea that he also would not have understood a city would contain women and children among it's citizens is complete idiocy. The authors give no evidence at all that Truman had reason to believe the cities only contained military personnel. I think people are misunderstanding the term "military targets" to mean targets that contained only military personnel and equipment. The entire war was full of bombing cities in efforts to take out the means of production, transportation hubs, etc. All "military targets" despite the presence of civilians.