The mention of Yahweh’s voice speaking “by the mouth of angels” is not a figure of speech or a scriptural allusion. It is a direct reference to the angelic communications to Alma and to Amulek (Alma 11:31).
By “them that are scattered abroad,” Alma continues Nephi’s interpretive practice of assuming that prophetic references to those on the isles of the sea meant his people. (See commentary accompanying 1 Nephi 19:24.) While we have few evidences of Book of Mormon prophets reading the scriptures, this allusion is another clue that Alma had read extensively in the Nephite scriptures: Melchizedek from the brass plates, here Nephi’s plates, at least those we know as the large plates. Of course, it seems likely that the prophets read at least some of the scriptures of the past; but Alma’s conversion was so dramatic that it seems likely that, in his thirst for information, he read everything available.