وَلَا يُؤَذَّنُ لِصَلَاةٍ قَبْلَ دُخُولِ وَقْتِهَا إِلَّا فِي الْفَجْرِ عِنْدَ أَبِي يُوسُفَ
Translation: The adhan is not given for a prayer before its time begins, except for Fajr according to Abu Yusuf.
Because adhan announces a prayer time, the general rule is that the time should have entered.
Abu Yusuf makes an exception for Fajr based on reports of a call being given before dawn. This exception does not extend to the other regular prayers.