Let not their conduct grieve thee, who run easily to disbelief, for lo! they injure Allah not at all. It is Allah's Will to assign them no portion in the Hereafter, and theirs will be an awful doom.
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.