Prayer times
Computed locally from astronomical algorithms — no third-party service.
How they are calculated
Prayer times are a function of date, latitude, longitude and the method you follow, so Qiyamah computes them rather than asking a service. That means they work offline and cannot break because someone else's API did.
Your location stays on your device. It is used to compute the times and is never sent anywhere but the calculation.
Choosing a method
The methods genuinely disagree, and the difference is not small. Fajr and Isha depend on how far below the horizon the sun sits, and the accepted angle differs by authority — 18° for the Muslim World League, 15° for ISNA, and so on. Umm al-Qura does not use an angle for Isha at all: it is ninety minutes after Maghrib.
Asr differs by school. The Hanafi position uses twice the object's shadow where the others use once, which is about an hour's difference — not a rounding.
Far north and far south
Above roughly 48° the sun does not descend far enough in summer for the twilight angles to occur at all. Where that happens the times are derived from a high-latitude rule and are labelled as derived rather than observed.
Scholars differ on how to keep prayer in those conditions. Qiyamah shows a calculation, not a ruling.