These invaders were the AMU or the HYKSOS who ruled Egypt during the centuries separating the MIDDLE KINGDOM and the NEW KINGDOM.
Josephus, the first-century A.D. Jewish historian, records the words of Manetho who wrote several books on the history of Egypt:
There was a king of ours, whose name was Timaus. Under him it came to pass, I know not how, that God was AVERSE to us, and there came, after a surprising manner, men of ignoble birth OUT OF THE EASTERN PARTS, and had boldness enough to make an expedition into our country, and WITH EASE subdued it by force, yet WITHOUT HAZARDING A BATTLE WITH THEM. So when they had gotten those that governed us under their power, they afterwards burnt down our cities, and demolished the temples of the gods, and used all the inhabitants after a most barbarous manner: nay, some they slew, and led their children and their wives into slavery. At length they made one of themselves king, whose name was SALATlS....and as he found in the Saite Nomos [Seth-roite] a city very proper for his purpose, and which lay upon the Bubastic channel [of the Nile], but with regard to a certain theologic notion was called AVARIS [RAMESSES], this he REBUILT, and made very strong by the walls he built about it, and by a most numerous garrison of two hundred and forty thousand armed men whom he put into it to keep it....THIS WHOLE NATION WAS STYLED HYCSOS, that is, SHEPHERD-KINGS....BUT SOME SAY THAT THESE PEOPLE [THE HYKSOS] WERE ARABIANS....” These people, whom we have before named kings, and called shepherds also, and their descendants,” as he [Manetho] says, “kept possession of Egypt 511 YEARS.” — Josephus, Against Apion, bk. 1, sec. 14. f.
http://www.hope-of-israel.org/amalekit.htm
Timaus was indeed a king over them — he was the Pharaoh Thoum who died at the Exodus, at Pi-ha-Khiroth / Pi-Khiroti. Thanks Fred Nerks.