What is the accepted procedure for setting an ADIZ? Large scale US and Russian naval and air exercises are common, they often involve a lot of airspace beyond national territorial limits, how is that handled? If there is lots of precedent for such requirements made by other forces during exercises, it will be hard for the US to object to China's doing the same.
Obviously the Chinese protests are because they hope to gradually get de facto acceptance of their territorial claims by setting up ID zones, anticipating that traffic has to conform to Chinese regulations. This seems like a low risk approach to building sovereignty.
The norm for exercises is to issue a NOTAM. Especial care is taken where these state they are live fire exercises. They could, of course, engage any aircraft which penetrate the NOTAM area, but that has far higher risks of its own.
ADIZ have no international legal basis. China has established one which, whilst being a matter of concern for airlines, is being ignored by the US forces and others. The US, UK and others have a tradition of deliberately challenging attempts by nations to use such means to limit transit of international waters and airspace - which is covered by international law.
East China Sea ADIZ
https://en.wikipedia.org/wiki/Freedom_of_navigation