What was the landmark event that turned the "public world" into the "family world"?

The change from "public world" to "family world" in Chinese history began with the establishment of the Xia Dynasty.

After the death of Dayu, his son Qi succeeded to the throne. Kai's accession to the throne was the beginning of the hereditary system of succession to the throne. In other words, the "public world" became the "family world.