When Jesus came with clear proofs (of Allah's Sovereignty), he said: I have come unto you with wisdom, and to make plain some of that concerning which ye differ. So keep your duty to Allah, and obey me.
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.