Don't forget that France also conducted nuclear tests among its possessions in the South Pacific Ocean. The UK tested atomic weapons in Australia and in South Pacific islands as well. Interestingly, it also tested weapons underground at the Nevada Test Site.
There were a handful of high-altitude tests conducted by the United States in the southern Atlantic Ocean as well.
In 1993, the UK government paid 20 million pounds to cover damage done during the Australian tests. It's also funded extensive remediation at the testing sites on and near smaller islands.
You might find this research paper from the Australian Parliament to be interesting. It covers the history of compensation for atomic testing in that country (at least through 2006.
I'd like to reiterate this question, but from an American perspective. Do we have data on reparations to pacific islanders subjected to American nuclear tests?
The big five nuclear powers — US, USSR, UK, France, China — all tested their weapons in remote territories of low-population density that they had control over. This often meant colonial territories, or territories inhabited by "subaltern" groups.
So the US tested its weapons in the Marshall Islands, which it had gained control over (from the Japanese) in World War II, inhabited by islanders. They also tested at the Nevada Test Site, land that was owned (via treaty) and inhabited by Native Americans until the Army seized it. The Marshallese suffered many medical maladies on account of the radioactive fallout they were exposed to. When they became an independent republic in the 1980s they were given a compensation package by Congress but in retrospect it was far too little to pay for their medical claims. The people most directly affected by testing at the Nevada Test Site were those who lived in towns like St. George, Utah, due east of it.
The Soviet Union tested in Kazakhstan, and produced many negative health impacts on the Kazakh people living nearby. They also tested in Siberia.
China tested in its western deserts (Lop Nur), on land inhabited by a Chinese Muslim minority, if I am not mistaken in my recollection.
The British tested both in the Pacific and in Australia.