It doesn't seem that either city knew with certainty that it was going to be subject to attack (nuclear or otherwise) on those specific days. Japan in general was experiencing relentless bombing. There were at least some evacuations in both cities, but these were not necessarily the result of the leaflets per se.
About Hiroshima, a Wikipedia page (the source it cites for this is behind a paywall) says that:
120,000 of Hiroshima's population of 365,000... evacuated the city
before the atomic bomb attack on it in August 1945.
However, this article says that:
The bomb, dropped by the US on August 6 1945, made orphans of around
2,000 children, mostly from central Hiroshima, who survived because
they had been evacuated to the countryside. [...] More than 90% of the
population of central Hiroshima perished.
The answer to this related question on Reddit states (without providing sources) that:
A large group of evacuees were in fact gathering in the center of
[Hiroshima] on the morning of August 6th, when the bombing happened.
About Nagasaki, this article from the US Dept. of Energy states:
A small conventional raid on Nagasaki on August 1st had resulted in a
partial evacuation of the city, especially of school children. There
were still almost 200,000 people in the city below the bomb when it