How the watches are showing perfect time?
Those 23hrs, 56mins, 4.1secs are actually the sidereal rotation period of Earth. It is how much time the Earth needs to perform one rotation relative to the stars. But that is not exactly the same as solar time. By the time the Earth has completed one rotation, it has also moved a little forward in its orbit around the Sun. Thus, it needs a few more minutes of rotation to catch up so the Sun is at the same location of the sky.