I doubt they'll stop at their home waters. What they consider home waters will just move more and more towards the US west coast. Right now the conflict is closer to them than it is to the USA but things may change rapidly.
China is being aggressive in the South China Sea because they're insecure about the US navy being so close. If things escalate then the US navy can start a blockade and stop virtually all trade between China and the outside world.
China wants to get control of the surrounding seas so its shipping routes aren't vulnerable to the US. That's also why they're investing so much in huge train networks through Asia and the Middle East – it means the US navy can't economically cripple them at will.
Or to use Occam's Razor: There's a greater density of assets to control, nearer at hand.
Edit : From a Chinese perspective, the Pax Americana has been a blip in history.
Over time, China will be looking to guarantee its SLOC(Se Linea of Communication(Control) for all of it’s global trade.
China is very vulnerable to economic harm from sea trade disruption.