No, that is a mischaracterization. The Hebrews did not believe Satan was a fallen angel but an obedient servant of God. Jews believe this to this day. The idea of Satan being a fallen angel is part of apocryphal Hebrew writings, and were accepted by apocalyptic Jews (including the Way). Such concepts as a fallen angel came from Persian influence on Judaism in the aftermath of the Babylonian captivity.
All references to Satan in the OT show him to be a servant of God. Inferences to Satan being the Phoenician king who though of himself as god, or of Babylonian morning star (which Jerome translated as "Lucifer," the shiny one) are not associated with Satan except through Christian teaching.
Christianity teaches that there is the Crafty One, the devil, the personification of evil, who out of envy fell from God's grace, and he is associated with every evil, including the god of Baal, Babylon's Morning Star, and the serpent in the Garden of Eden. He represents all the evil, and whatever is evil becomes him, including us.
I guess Jesus was confused, for He referred to him over 15 times and never in a good way. Plus Jesus bound him up
Luke 10:18
And he said unto them, I beheld Satan as lightning fall from heaven.
And why did He bind him? Because
1 Peter 5
Be sober, be vigilant; because your adversary the devil, as a roaring lion, walketh about, seeking whom he may devour