A two to three kiloton nuclear explosion approximately 100 miles east of the island would not be noticeable. The prevailing winds blow east, but the nearest islands are another 400 miles away.
The coordinates of the blast are given as 47°S 40°E, while Prince Edward is at about 38°E. Google maps shows the distance as about 100 miles. Tan(2degrees) x 100 x 5280 gives about 18,400 feet below the horizon at Prince Edward for the elevation of the blast. So any radiation from the blast itself would travel through a lot of shielding water and rock. Possibly the decay of fallout aloft could be detected, but that would only be for gamma radiation at that distance through air. And not many fission products would make it to 18,000 feet from a small bomb.
Prince Edward island is only 12 miles or so from Marion and visible from the base so it certainly did not happen in the waters between them.