What oscillator are they using? Things like the DS3231 (which are temperature-compensated crystal oscillators) only do about +/- 2ppm, which is about +/- 1 seconds per week. You can tune them to do better (mine has been running at about -0.007ppm for a while), but on the tin, they appear to be worse than what you reported. (And they go to great lengths to be that accurate.)
My main conclusion is that I want a watch with one of these in it: https://www.microsemi.com/product-directory/embedded-clocks-...