I don't know where you get this, for the second Adam is the one through whom we attain that rest. You will have to define the term
Adamic men are the descendants of the mortal Adam. The ancient Jewish belief which I am describing here is that he was appointed 7,000 years in parallel to Creation week and his banishment - the last 1,000 years being the Sabbath, Christ's reign on earth. Thus concludes the "realistic, national" promise.
Last Adam:
When the 7,000 year calendar is over, this heaven and earth will be gone, replaced by the new heaven and the new earth populated by those of us whose names were written in the book of Life of the Lamb from the foundation of the world. Thus concludes the "transcending, universal" promise, the preexistent Messiah, Jesus Christ by Whom and for Whom "all that there is" is.
It is not an either/or - not for the Jews (who cannot see the later) - and not for us (who sometimes cannot see the former.)