The connection between Athen's Eleusinion and the Eleusinian Mysteries is supported, for instance, by another passage of Clement of Alexandria's Protrepticus (3. 45.1), where he tells us that the tomb of Immaradus, son of Eumolpus (the mythical ancestor of the Eleusinian hierophants), was there.
There is also epigraphic evidence for the connection between the Eleusinion in Athen's agora and the Mysteries, see for instance
Clinton, K. 1980. A Law in the City Eleusinion Concerning the Mysteries. Hesperia: The Journal of the American School of Classical Studies at Athens 49.3:258-288.