The remnant came from people who frequently received a place called "this land" in the prophecies. For example: "we have obtained a land of promise, a land which is choice above all other lands; a land which the Lord God hath covenanted with me should be a land for the inheritance of my seed. Yea, the Lord hath covenanted this land unto me, and to my children forever, and also all those who should be led out of other countries by the hand of the Lord." (2 Nephi 1: 5.) The relevant "land" is one which the ancestors of the remnant were promised would be choice above all other lands. A land of inheritance for the remnant. And one to which people would be "led out of other countries by the hand of the Lord" to later occupy. This is a reference to Nephi's earlier vision wherein the unfolding history of the Americas were shown to him. That included the following:
There would be a man separated by "many waters" who would be wrought upon by the Spirit of God and make the journey across the "many waters" to the remnant "seed of my brethren, who were in the promised land." (1 Nephi 13: 12.) This identifies Columbus, whose original landfall was in the West Indies of the Caribbean. However, the prophecy continues with greater details, increasingly focusing on a North American setting.
After the original discovery by the man wrought upon by the Spirit of God (Columbus), the same "Spirit of God... wrought upon other Gentiles" who also made the migration across the "many waters." (1 Nephi 13: 13.) Again it is not unequivocal because migration included and still includes both North and South America.