We bombed Hiroshima 6 Aug 1945
The Soviet Union declared war on Japan and invited Manchuria 8 Aug 1945
We bombed Nagasaki 9 Aug 1945

Most historians appear to believe that the Soviet actions were not in response to the nuclear attack, but rather based on Stalin's commitment to declare war against Japan within 3 months after VE Day.

So if it didn't affect Stalin, how did that timing affect Truman's decision? How much did he fear that a prolonged invasion of Japan would give the Soviets time to get involved in a major way and create puppet states?