Oh,so you are saying that:
1-Adel was interested in Ellone for being her successor.
2-Odine researched her powers and discovered her ability.
3-Odine created Junction Machine Ellone.
4-It reached Ulti and she used it to take over the world.
5-She then possessed Edea first.

So Adel is not possessed isn´t it?

Well for those who believe in time loops it would not be difficult to see that Adel could have been possessed by Ulti.I always thought it was implied in the game.