The UNCLOS & EEZ laws did not formalized until 1982. So if all Vietnamese holdings in Spratly Islands occupied prior to 1982, then they are not affected by UNCLOS.
People also confuse about sovereignty of Spratly Islands and EEZ. If I interpreted the case which Philippines brought against China correctly, it is about China's Nine-Dashed-Line (claimed of sea and its natural resources) overlapped with Philippines' EEZ.
As for sovereignty issue of Spratly Islands, I think France made the earliest claim to the Spratly Islands chain. Since Vietnam being the successor state of French colony, it is most likely to be considered to have the earliest claim. At the end of WWII with new world order, ROC made the claim to Spratly Islands, most likely with consents from winning Allied powers since both US and France didn't object when ROC made the claim nor when Japan renounced the Spratly Islands to ROC in the 1952 Treaty of Taipei. Last came Philippines. When Philippines was still American or Spanish colony, they didn't make the claim to Spratly Islands. Also, since Philippines occupied Thitu Island is both outside of Palawan's EEZ and predated 1982 UNCLOS, that would be contradictory to Philippines' case if they forced the issue about occupation prior to 1982 UNCLOS.