This depends on which masjid you believe is calling the Athan on time. A lot of masjids call the Athan few minutes before the real time so that people would stop eating in Ramadan. This is wrong because if people pray, their pray would be invalid because it was done before the proper time.
Therefore, I suggest that you don’t pray the Sunnah until the last one calls for Fajr.
And Allah knows best