Higher end watches also get external certifications that reflect different precision standards. Some examples: METAS, COSC, or Rolex Superlative Chronometer if you are Rolex and need to be special. They have different specs, Superlative Chronometer is +/-2 sec per day. If it's out of spec and you're under warranty, you may be entitled to a free adjustment by a service center. Otherwise, overtime, as the performance degrades, it's a signal you may need a service.
There's also the risk of magnetization. If the delicate machinery becomes magnetized, you'll see BIG swings, like +/- minutes per day. Demagnitization is something any watchmaker can do quickly. (There is inherently some risk posed by the phone itself having a lot of magnets, but modern watches are typically built to resist magnetization to varying degrees -- look at the Rolex Milgauss as an example of best-effort magnet resistance)
Watches will also perform variably depending on position. If you know your watch is -4sec/day on your wrist, but +6sec/day face down, you can effectively manage it's accuracy by placing it face down over night and never have to unscrew the crown but keep a true time. This is a very common use case.
Hope that covers the general cases. This app avoids a lot of even deeper complexity, like beat error and amplitude which are deeper metrics describing the movements performance and guide watchmakers to know which screws to adjust which way.