You're still getting the "islands in the EEZ" vs "EEZ is defined by the islands" backward. The EEZ doesn't define what islands are controlled. The land, including islands, define the EEZ. Also, a EEZ doesn't automatically extend out to 200 nautical miles from the island. It extends out to a maximum of 200 nautical miles, but may stop when it first it runs into someone else's EEZ. Often you'll find EEZs that extend exactly half way between the "defining" features.

Fiery Cross is typically defined as a "reef" under the UNCLOS. According to most of the sources I can find, it was below the high tide mark before it was built up by the PRC. As such it has no territorial sea or EEZ of it's own, and should fall under the nearest island's EEZ. Veitnam seems to claim that the nearest island is either Spratly Island or Sin Cowe Island, I can't recall exactly how their claim is stated. As such, Fiery Cross should be part of the EEZ defined by the two islands, and thus part of Vietnam's EEZ. This would make China's activity on Fiery Cross inside Vietnam's EEZ and thus an infringement on Vietnam's territory. In order to be consistent with Vietnam's claims on their other islands, the must protest any Chinese activity on Fiery Cross. That all said, Vietnam's protests do often sound a bit over the top. No question that in order to be valid, Vietnam's claims must be in agreement with the terms of the UNCLOS. And there is no question that Vietnam is interpreting their case in the most favorable light possible to Vietnam. None of that in and of itself is a a major problem to opening negotiations, or taking the claims to arbitration.

The UNCLOS is a bit vague as to what characteristics make a feature capable of "sustaining human habitation", or "an economic life of their own". Nothing in the treaty specifically states that a natural source of water must be there to be called an "island". Rain water capture is often used on many islands that lack natural springs to sustain human settlements. This is quite common in certain regions, like the Caribbean. However, the UNCLOS does provide for arbitration, in the case that the claimants can't agree on what is an island and what is a rock. So far the PRC refused to agree to attend any such arbitration, and has adopted a highly hostile attitude toward the possibility of an arbitration ruling. This is a problem, and allows the other claimants diplomatic cover for their complaints. If Veitnam tried to take their current claims to arbitration, much of it would simply be rejected as not valid. Veitnam would have to back peddle and it would be highly embarrassing. It is highly unlikely that Vietnam would receive global support for claims that were rejected by a neutral arbitrator, and there is very little that Vietnam could do without outside support. There is virtually no way that the US or it's allies would want to get involved in the dispute on that side of things. The US has no desire to go to war with China and all of the expense that that would entail. If China is behaving responsibly, the US would tell Vietnam to moderate it's claims. So far China's lack of willingness to call for such has allowed Veitnam to get away with it's activity.

The worst part of the whole deal is that China's current diplomacy is very counter productive. It has destroyed much of the good will that the "peaceful rise of china" narrative provided. Now nations don't see China as a potential counter to the US, but as a regional competitor to themselves. That in turn fuels the perception of the US as a potential counter against an unreasonable PRC. The PRC's great size, power, and unreasonable claims have caused nations like the Philippines to gloss over or ignore their similar disputes with the Republic of China and Vietnam, simply because they risk loosing it all if they don't. The Philippines's current arbitration case against China makes that very very clear. At the same time, the US is watching the PRC be very unreasonable with it's neighbors, and thus expects the PRC to be unreasonable with the US as well.

All around this is a bad deal for everyone. The part that has me stumped is why in the world is Beijing doing this? From my prospective it looks like madness on the part of the PRC!