Note that this "study guide": https://www.studymode.com/essays/And-Then-There-Were-None-My...
gets the name of the island wrong: it's "Soldier Island."
For obvious reasons, that title was considered unsuitable for sale in America, so American editions were renamed to And Then There Were None, and the island and poem were changed to reference (depending on edition) Indians or soldiers instead. Most editions these days have settled upon soldiers.
Incidentally, Wikipedia mentions one use of the phrase “our black brothers” that only makes sense in the context of the original naming.
Whilst there are several islands off the coast of Devon, hers was a fanciful creation. The entire story just revolves around poem.
Perhaps they mean "Vera Claythorn becoming semi-hysterical" only makes sense knowing the name, but that's a bit of a stretch.