The THAAD system comes with an extremely high range AN/TPY-2 radar that can easily be configured to surveillance the northeast of China (and you can bet the US military will just do that), which besides Bejing and Shangai also is where most of the Chinese military is based including their Headquarters. And that's a radar that's able to detect missiles, in FBR mode it can also easily pick up any plane etc. The missile system isn't the problem (it couldn't shoot down any missiles launched in China that are aimed at targets outside Korea anyway and can only fire in a limited arc facing towards NK), the radar system is:
Just imagine if China was stationing one of those things in Cuba. You'd get one hell of a harsh reaction too and severity of the threat to the US wouldn't be even comparable to what the AN/TPY-2 deployment means to China.
Recently held a presentation on the topic in my international politics class, if there are questions I might be able to answer them.