Vassal relationship is symbolic, not territorial nor economic(no regular taxes to pay.) Mongol Empire was an exception to this.
You mean, China had some outlying administrative areas in Liao-dong/Liao-shi back before 4th century AD. It was not near Pyongyang area as some argue.
This things come and ago. This area changed hands many times.
Old Chosun had it. Han Dynasty had it. Xianbei had it. Koguryo had it. Balhae had it. Khitan had it. Jurchen Chin had it. Mongol had it. Ming Dyansty had some garrisons there.
It goes on.
Korean claim to Changbai mountain is a wet dream!