A deus ex machina is generally undesirable in writing and often implies a lack of creativity on the part of the author. The reasons for this are that it does not pay due regard to the story's internal logic and is often so unlikely that it challenges suspension of disbelief, allowing the author to conclude the story with an unlikely, though perhaps more palatable, ending. Like the PC becoming Arch Mage after being in the mage guild for like a week.
And another trait of a deus ex machina is that it leaves the question why it didn't intervene earlier.
In this case - Why didn't they teleport the eye away in the moment it was found? If they have the authority to appoint an amateur spellcaster to be the headmaster of a mage college, why didn't they just show up and demand the eye before it could cause trouble?
Of course all of this could have been an ingenious plot of the Psijics to get their hands on the eye, without causing too much trouble (for them). The incompetent archmage will keep the college busy for years to come, and nobody thinks twice about another missing Thalmor in Skyrim. Enough stuff for an expansion (or mod).