Building a nuclear reactor in the South China Sea is a dangerous undertaking, and most countries in South-East Asia will be unhappy. Enough said about serious problems at Fukushima & Chernobyl melt downs. I believe that most countries are wary about the building of nuclear reactors, regardless of claims of safety & expertise of the builder of whatever country it maybe.
You do understand that a ship based nuclear reactor can go anywhere it likes and isn’t rooted in place right? That is the whole point - rather than trying to make a weather proof nuclear reactor, China will simply sail said reactor out of the way of any storms that might threaten it. Being ship based would also make it immune to earthquakes and tsunamis. That pretty much covers all natural threats to nuclear reactors.
As others have pointed out already, countries sail nuclear powered carriers and subs in the SCS all the time, if those countries had no problems before, they have no reasonable groups to have a problem now.
Countries in SE Asia has precisely as much say about China building a ship based floating nuclear reactor as they do about China/America/Russia/Britain/France etc building nuclear powered subs and ships.
Similarly, they have precisely as much say about China sailing said floating nuclear reactor into the SCS as they have aboutChina/America/Russia/Britain/France etc sailing nuclear subs and carriers into the SCS.
If they want to restrict access of the floating Chinese reactor, then they need to get on China’s side on freedom of navigation vs rights of coastal states.