Praise be to Allah.
If the mu’adhdhin gives the adhaan at the usual time of the adhaan in your city, which is based on the common timetables, and he does not give it later than the time given in the timetable, whether that is due to a mistake on his part because he is not precise, or it is based on his own ijtihaad and opinion – rather his adhaan is in accordance with the timetable that is used in your city – then there is nothing wrong with your relying on his adhaan, even if it is later than the time given in the timetable of the program mentioned.
But if the mu’adhdhin is not known to be careful and precise in following the timetable, then in this case you cannot rely on him, and you can rely on the timetable of the program mentioned.
However, to be on the safe side in all cases, you should pay attention to the timetable of the programme, because it is known that this program is precise and trustworthy.
That is because making the mistake of being too early and refraining from eating and drinking a few minutes before the adhaan is less serious than the mistake of eating and drinking when dawn has broken, based on the other timetable.
Shaykh Ibn Baaz (may Allah have mercy on him) said:
If he hears the adhaan and knows that the adhaan is usually given at the time of dawn, then he must stop eating and drinking. If the mu’adhdhin gives the ahdaan before dawn breaks, then he does not have to stop eating and drinking; it is permissible for him to eat and drink until it becomes clear to him that dawn has broken.
If he does not know whether the mu’adhdhin gives the adhaan before or after dawn breaks, then to be on the safe side it is better for him to stop eating and drinking when he hears the adhaan, and it will not matter if he eats or drinks something at the time of the adhaan, because he does not know whether dawn has broken.
It is well-known that those who live in cities where there are electric lights cannot know whether dawn has broken from looking, but to be on the safe side they should follow the adhaan and timetables which state the time of dawn in hours and minutes, acting in accordance with the words of the Prophet (blessings and peace of Allah be upon him): “Leave that which makes you doubt for that which does not make you doubt” and “Whoever guards against the doubtful matters will protect his religious commitment from shortcomings and will protect his honour from slander.”
End quote from Majmoo‘ Fataawa Ibn Baaz (15/286)
And Allah knows best.