At the time it came to resolve the war, Japan was forced to remove itself from various occupied areas including but not limited to Korea, China, and Pacific Islands.
For instance in the Cairo Declaration it was stated that:
"Japan shall be stripped of all the islands in the Pacific which she has seized or occupied since the beginning of the first World War in 1914, and that all the territories Japan has stolen from the Chinese, such as Manchuria, Formosa, and The Pescadores, shall be restored to the Republic of China. Japan will also be expelled from all other territories which she has taken by violence and greed. The aforesaid three great powers, mindful of the enslavement of the people of Korea, are determined that in due course Korea shall become free and independent."
Note that here the United States, Britain and China together recognized Manchuria, Taiwan and the islands off of Taiwan as Chinese. Japan would need to extricate itself from Korea.
The Qing Dynasty, before the war, had explored and occupied the Paracels and the Spratlys - to a minimal degree, since it had never become a great naval power. Indeed, there are a number of instances of Vietnam and China 'trading' the Paracels back and forth to protect their ownership during the occupation of French Indochina.
These islands had also been occupied by imperial Japan (such islands are useful in naval warfare), who was forced to remove itself. The Potsdam Declaration reads "Japanese sovereignty shall be limited to the islands of Honshu, Hokkaido, Kyushu, Shikoku and such minor islands as we determine." These islands were very limited indeed, did not include the Paracels/Spratlys and it should be noted that they do not include the Kurils (something today that the Americans would like to revise history on).
Similarly, section (f) of article 2 of the Potsdam Treaty reads of Japan: "Japan renounces all right, title and claim to the Spratly Islands and to the Paracel Islands."
What we have is a situation where the Philippines never had administration or territorial claims to these islands and where the Qing Dynasty had. In the post-war period, China was not only weak, but could not spend much patrolling the South China Sea - and focused primarily on it's Western Front during the Cold War.
Today, China is trying to build infrastructure, shipping routes and naval security in this area. This is important to China because of its historical vulnerability to naval embargo, through the Strait of Malacca and elsewhere.
The United States had hoped, because of weak territorial enforcement during the postwar period, to make an issue over the ownership of the islands and waters as part of a geopolitical effort to limit the expansion of Chinese influence in an area historically militarily dominated by US projection (it's own National Security concerns pertaining to its continued naval access to potential adversaries and compeditors).
The bulwark of that effort was an attempt to build an Asian consensus, centered around the Philippines (an important US ally and prior colony). However, the effort failed, with states in Asia fracturing in opinion and not willing to commit themselves to a United States led effort to persist its power projection in that way.
This is still evolving of course, but the future looks rather dim with the Philippines (the keystone of the project) backing away.