404, with all due respect that is incorrect. Adams Park's northern boarder is Cascade Rd. If you travel down Cascade Road you see the stone pillars identifying the neighborhood as Adams Park on the corner of Sandtown Rd and another at Blvd Lorraine.
Cascade Rd is the Northern boundary, Centra Villa is the Eastern boundary, A short segment of Campbellton Rd is the Southern boundary, and the Western is Willis Mill Rd. On the shorter Campbellton Rd segment most of that is the Golf Course not homes.
Also, it is very common for complexes to use the name of a nearby upscale community in its name. Some if not all of those apartments you mentioned are not in Adams Park proper. A general rule for that neighborhood is if there is not a street topper identifying it as "Adams Park" is probablly isn't Adams Park. Think of how many places in Smyrna and Mableton have "Vinings" in their name. This also happens a lot with Brookhaven and East Atlanta.
Here's a map of Adams Park.
Adams Park Map