It has all sorts of different layers. The gods appear to people routinely. People are in contact with their gods. And then he starts. But that's an interesting measure of how common the expectation is that gods appear.
Gods appear in dreams.
People fall asleep every night. So there's a contact between heaven and Earth that's articulated in terms of traditional Roman and Greek culture. Some kind of ancestor worship, or perhaps if you were an aristocratic Roman, Venus or one of the other gods might be, as with Julius Caesar's family, might be one of the founding ancestors of your particular household. You would have the gods of the city, itself. And it's those city gods, in combination with the gods of the Empire, that would structure time for you.