The order did originate from Xemnas, and went through Saix. However, Saix wants it for his own purpose.
Finding the Chamber of Waking as well as eliminating the traitors in CO could both be used to serve Saix and Axel's "plans."
Interestingly, Nomura stated that Xemnas probably knew that Saix wanted to betray him in the end. However, he never really had the chance, as Saix suggests in one of his secret reports, because circumstances prevented him from doing so.
why would the chamber be important to Saix? does he know (or does anyone know) for sure that "the other friend" is asleep in there?
and, aqua is the only one who can unlock the chamber, right?