If both of those claims were the case (we really don't know that much about the meetings), the question of interpretation is still open, i.e. was this used to beat down the Army's resistance to surrender, since even more so than in 1938-9, the Red Army was going through them "like crap through a goose", to use the famous Patton quote.

Everything I've read indicates that it was the second bomb, which indeed happened on the same day as the declaration of war, that really got the attention of the rulers of Japan, and got them serious about surrendering.