Praise be to Allah.
What matters with regard to breaking the fast is the setting of the sun, as the Prophet (peace and blessings of Allaah be upon him) said: “When the night comes and the day departs, and the sun sets, then it is time for the fasting person to break his fast.” Narrated by al-Bukhaari (1954) and Muslim (1100).
What is meant by setting is when the disk of the sun disappears. No attention is to be paid to the red glow that remains on the horizon. So when the disk of the sun disappears, then it becomes permissible to break the fast.
Most of the muezzins nowadays rely on timetables, and there is nothing wrong with that, but some of them fall short in making sure that their clocks are accurate, as they should.
If the muezzins differ, then you should either see which of them is more precise in timekeeping and gives the adhaan at the beginning of the time, not too early or too late, and rely on his adhaan and no other;
Or you can rely on timetables yourselves, after making sure that your clocks are accurate, even if the muezzin has not yet given the adhaan.
And Allaah knows best.