The Americas have no place in classical astrological chorography, and the reason is simple and total. The scheme divides the oikoumene, the inhabited world known to a second century Greek writing in Alexandria, and the Americas were not in it.
This is a different situation from a gap in a record. There is no lost passage, no disputed reading and no competing tradition to weigh. Ptolemy's four quarters cover a landmass reaching from the Atlantic coasts of Europe and North Africa to India and central Asia, and the whole of the western hemisphere lies outside the frame. No quarter, no triplicity and no planetary co-ruler was ever assigned to it by the tradition that built the scheme.
Later astrology has filled the gap in various ways, and none of them carries the authority the classical assignments do. Mundane astrologers work from national charts instead, most famously the several competing charts proposed for the United States, which disagree about the rising sign and therefore about almost everything downstream of it. That is a live dispute among practitioners rather than a settled assignment, and it operates on nations rather than on a continent.
The atlas records the absence as an absence, with an open question attached to it, rather than supplying a plausible looking ruler that no source supports. A fabricated entry in a correspondence table is worse than an empty one, because a table is read as a record.
Sources TetrabiblosClaudius Ptolemy with A History of Western AstrologyNicholas Campion