Why did the days get shorter after beginning of autumn?

In the northern hemisphere, the daytime becomes shorter after beginning of autumn and longer after beginning of autumn.

Beginning of autumn is between the summer solstice and the autumnal equinox. When the summer solstice points to the autumnal equinox, the days in the northern hemisphere continue to shorten until the autumnal equinox is equal. The days in the southern hemisphere continue to increase, and the length of day and night is equal to the autumnal equinox. Therefore, the days after beginning of autumn in the northern hemisphere will be shorter.

Beginning of autumn is the first solar term in autumn, which falls on August 7-9 of the Gregorian calendar every year. It means precipitation, humidity, etc. It is at the turning point of the year and tends to decline or decrease.