You used a device like that described in the parent article to measure the deviation from the correct frequency and you adjusted the frequency with a fine screwdriver or a similar tool, until measuring the desired nominal frequency.
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.
The objective is to minimize this number as much as possible. The open source sensor watch has a temperature sensor and software which turns it into a temperature compensated quartz watch. Mine loses time every year instead of every day or every month.
Man with two clocks, never quite sure...