Dr. Wilkerson informs Thatcher a 24-hour guard will be posted, and he wants him to stay and watch over the "mummy". After Herman awakens and opens the lid, Thatcher flees from the room. But there is no guard present to notice Herman leaving.
Even within the Munster fantasy parameters, there's no obvious reason why the stuffed gorilla should have come to life as it did.
Since Herman is able to pry open the sarcophagus when he believes it is a telephone booth, he could have easily pushed it open when it tumbled over on its back with him in it.