Answer: One denomination believes Satan was cast out of heaven in 1914 A.D. when World War I started! This is, however, clearly not true. Though it was a pivotal year in world history, the great tribulation did not start at that time nor did the Second Coming occur. God's adversary Satan, who is also the enemy of all mankind, was removed from heaven many years prior to 1914.
One foundational verse that gives us a period for when Satan was cast out of heaven is in the Scriptural reference you wrote about in your question. The context of the statement is that the seventy men the Lord sent out on a gospel training mission had returned to him. The first recorded thing they said to him was, "Lord, even the demons are subject to us . . ." (Luke 10:17).
Jesus' response to their amazement was a profound revealing of who he was and the life he had before becoming a human (it also is one of many proofs that he is God).
Jesus confessed that he personally witnessed the quick and powerful casting out of Satan, with all the speed of a lightning bolt, from the presence of his Father's throne. He said to his disciples, "I was watching when Satan fell from heaven like lightning" (Luke 10:18, HBFV).
Satan the devil was speedily cast out and ejected from the third heaven, the true center of the universe, long before what happened in Genesis 1:2 took place. His revolt took place when he was on the earth carrying out responsibilities he had been given.
In Isaiah 14, we discover that he planned to ascend to where God resided (which means he was not already there!). What was he planning to do once he reached the power that brought everything into existence? He planned an all-out assault, with his army of deceived angels, to forcibly take control of God's throne so that he could rule everything (Isaiah 14:13 - 14)!
Before his sins of vanity and lust, plus his rebellion, got Satan cast out from God, he was a powerful covering cherub (a special class of angels) right over the throne of the universe (Ezekiel 28:14 - 15). God, while he was still obedient, put him on the earth with certain responsibilities.
Satan then, with one third of all the angels that existed, decided to become the enemy of all righteousness (Revelation 12:3 - 4). As his planned attacked reached the Eternal he and his angels were thrown back to the earth. This is the event Jesus witnessed.
Satan, whose heart is dedicated to evil, will try at least three more times to rise up from the earth and attempt to take over the universe. His second attempt to take control of all things will happen prior to Jesus' return to earth! If some teach this event has already occurred they are flat wrong. Christ did not come back to the earth, secretly or otherwise, in 1914 or any year since.
Satan the devil's third attempt is what the Bible labels as Armageddon. His final attempt at grabbing power, which will also utterly fail to remove God from governing all things, will occur after the millennium when he is loosed for a short period (Revelation 20:7 - 9).
On a final note, many believe that after being cast out of heaven that Satan (or other demonic spirits) are not capable of dying because they are composed of spirit and therefore indestructible. This flies in the face of Scripture which records demons knowing that they can be put to death (see Mark 1:23 - 25). They are fully aware that many, if not most, of them are going to be put to death forever in a lake of fire.