I can see why you might be confused, but the mythical story of Aegyptus should not be confused with the historical reality of Hellenistic (and Roman) control of Egypt. Hesiod (ca. 700 BCE) recorded his mythical history of Egypt in Greek terms, but he would not ever have claimed that Hellenes had controlled Pharaonic Egypt, which had been independent for nearly two millennia, and was the "super-power" of the eastern Mediterranean, especially in comparison to the small city-states of ancient Greece.

Here is a brief summary of the interaction between Greeks and Egyptians. There had been some trade between New Kingdom Egypt and the Mycenaean Greek Aegean in the 15th-13th centuries BCE, but that ended with the collapse of the Mycenaean kingdoms in the Late Bronze Age, around 1200 BCE. In the 8thcentury BCE, trade resumed and a small Greek trading colony (Naucratis) was established in the Nile Delta, at a time when Egypt was experiencing political turmoil during what we call its Third Intermediate Period. After Egypt was conquered by the Assyrians, Greek mercenaries were employed in 653 BCE to help establish the Egyptian Saite dynasty. Again, in 570 BCE, other mercenaries from at least nine different Greek city states were employed in a dynastic struggle between the Egyptians Apries and Amasis II, and even though they fought on the losing side, they were settled at Naucratis, which became a real city at this point in time, although one under the control of the Egyptian rulers. In 525 BCE the Persians conquered Egypt and controlled the Nile until the final independent Egyptian dynasty ousted the Persians in 402 BCE. Throughout the 6thand 5thcenturies BCE, Greeks such as Solon or Herodotus traveled to Egypt to marvel at its ancient wonders and history. The Persians briefly regained control of Egypt in 343 BCE before Alexander’s conquest of 322 BCE. Alexander, however, never ruled in Egypt, which came under the control of one of his generals, Ptolemy, who formally became king of Egypt in 305 BCE.