Once you and Tolfdir have fully entered the room, a strange glowing mote will descend from the ceiling. Moments later, the entire room goes grayscale and a strange man- an Elf of some sort apparently- will appear behind the podium. He wears a robe unlike any seen elsewhere in Skyrim, and he warns you that by entering the tomb you have started something that cannot be stopped. This is not a punishment or judgement, he cautions, as you had no way of knowing what would begin here.
What judgement there is, apparently, waits upon your response to what you find and experience here in Saarthal. You have been warned because the Psijic Order, whoever they may be, believe in you and are watching you. You, according to the man (who identifies as Nerien) are the only one who can handle whatever it is. His speech done, the Psijic mage vanishes, and Tolfdir becomes active again.
Your teacher turns to you and remarks upon the odd feeling he just got, asking what happened. When you tell him of the apparition, he admits that he didn't see anything at all. He would, however, like to know what it is that you saw. Your reply that you were told of pending danger and the Psijic Order surprises him, prompting him to mention that this is strange and the idea of danger ahead is a bit absurd.
He considers the Psijic Order being mentioned very strange, as they haven't been seen nor heard from in some time and really have no involvement with the ruins here to begin with. He asks that you help him to inspect the coffins here, dismissing the odd apparition in the interest of seeking out discovery within the ruins. You can now ask Tolfdir about the Psijic Order.
He will explain that the Psijic Order is a group of mages whose origin predates the Empire, and they and their island vanished some time ago, to be mostly lost to history. He cannot think of anything that they may have to do with the ruins here. As to what they want with you he cannot say. He isn't sure that you have actually been contacted by the Psijic Order, but with their island having vanished a century ago and their being a very exclusive group he asserts that you may as well take their interest for a compliment- the Psijic only contact those they consider 'worthy', by whatever measure they use.