刻 means ''to carve'' but my dictionary also says it means ''to set a time limit''.
well, you need a better dictionary 😼
in 國語辭典, the first explanation of the entry “刻”, as noun is:
「刻」 originally referred to the carved markings which recorded water levels throughout the day, as a substitute for time, on the cylinders of elaborate systems of water flow like the following:
「刻」 being equal to a quarter of an hour comes from a time division system on the water clock which divides a day into 96 「刻」.