McElveen Family Genealogy Forum
I do not have absolute documentation that Adam is the son of John. The history of the McElveens in SC in the early 1700s is very sketchy to say the least.
Winston H. McElveen of Hartsville, SC has done a tremendous amount of work on this family. He has a book "The McElveens of South Carolina". If you can get a copy of his book it can answer most of your questions on the McElveens. For a connection of John and Adam, see pages 34 and 35.
I hope this is helpful.