The supernatural events in Julius Caesar are very much part of ancient literature. The Romans were very aware of supernatural events such as prodigies and omens. They believed that the gods communicated with them through these. We can say that they were like signaling mechanisms with the divine. This might seem strange to modern readers, but it is only in the west and only recently that people shied away from the supernatural. Even in Shakespeare's time, people had very strong beliefs in the supernatural. So, I would say that these supernatural events fit right in the narrative and also fit into the culture of readers with perhaps the exception of modern times.