You don’t understand logic.
It does not make Korea part of China because certain Korean dynastic families paid tribute to certain Han families hundreds or thousands of years ago.
This is ChiCom logic.
They took over Tibet based on this logic (because Tibet was easy to take over).
When Xi says this he is saying China still has suzerainty over Korea.
“They took over Tibet based on this logic”
No, they merely justified their takeover with this logic.
There is no law in any of this, merely power.
“When Xi says this he is saying China still has suzerainty over Korea.”
Yes, exactly. That will be his, and their, argument if they do end up squeezing either North Korea or South Korea.