The Chinese Warship, and the USNS Bowditch, were not in Subic Bay. This incident took place 50 nautical miles north west of the Subic Bay Maritime Area, outside of Philippines Territorial Waters.
There are extensive contentions over which country can claim water ways in the South China Sea. The primary driver of this contention is China's belief that their territorial base line should be structured off of islands they claim ownership of well beyond the nationally recognized baseline.
As of late, China has been reinforcing reefs and recovering islands, including adding anti-aircraft armaments to these man made islands. Similarly, the Philippines Navy has Sailors 'stationed' in a rusted out ship stranded in the reefs of the Spratley Isles to protect their claim.
This is a rough map depicting the disputes of the South China Sea.