In "The Door" (Game of Thrones, S06E05), we see that Bran Stark has a vision where he sees the army of dead. The army doesn't see him, they are just still, but once he approaches the Night King, he observes the Night King looking at him. As he turns back, the army is also facing him, the Night King is standing behind him and later the king also touches his forearm.
One thing I don't understand is: it was Bran's vision, so how could the Night King see him? Is there any reference to such a power from the Night King in the book or series?