Had Allah willed, He could have made them one community, but Allah bringeth whom He will into His mercy. And the wrong-doers have no friend nor helper.
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.