If we watch EoE, we all remember those awesome multitudes of Rei. These did not actually exist, they were merely "visions" or "flashbacks" that became others.
In the same way, the "Adams" from 2.22 were in the same respective way; They were merely visions. Adam being a Progenitor of Life, these visions of the FAR would be visible to others as well, including Katsuragi-san.
In Rebuild, I have two explanations for Adam. Obviously, the white thing underground is Lilith. This will never change. However, in Rebuild, there are two different possibilities for Adam.
The first, obviously, is the Key of Nebbuchanezzar. In the original TV run, the Second Impact reduced Adam to an embryo. Rebuild takes this up a level and reduced Adam to nothing more than a nervous system.
The second possibility is the EVA-Mark.06, sometimes viewed as the "True Evangelion". (However, Unit-01 may also hold this title) If we recall the scenes from the moon regarding her construction, Seele's Eva is nothing more than what appears to be a Black Lilith. It is possible that the Progenitors of Life all look the same, their colours and small designs being the only real difference.
In 3.0 and in Final, I can almost garauntee that either of the above is going to be Adam. The KoN serves no real purpose yet, but Ikari may be planning to use it as the Backup in case all of the Angels were destroyed, and would still be able to initiate Third Impact.
"When the going gets rough, the fighters fight harder." -KSL
"Perpetual change is stasis." -KSL