When did the whole human race fall under Satan's control?
The whole human race fell under Satan's control when Adam sinned. That is the point in the context: Adam's transgression brought humanity under Satan's dominion, and the cross of Calvary is where Christ paid the redemption price to bring people back. Redemption was necessary because of that fall.
Les explains that for the whole world population in general, Christ paid the price with His own blood. The cross of Calvary is where Christ paid the price of redemption so that the whole human race, which fell under the control of Satan when Adam sinned, could be redeemed. He paid the price for every human being's sin, but a person cannot appropriate it until faith comes into the picture. The blood is the price of redemption, and without the shedding of blood there is no remission. Israel's redemption from Egypt was more symbolic than actual, but for the world Christ paid with His own blood.