There is nothing to reconcile with regard to God's sovereignty, for he is the Almighty, the only true God, the maker of Heaven and Earth. Only those who contest or doubt the idea that God is sovereign, who think that the presence of Satan as 'god of this worldly system' somehow invalidates God's claimed sovereignty over all creation, would think there's a need for reconciliation. The need is for us to be reconciled to just who God really is, by rejecting the deceptions and lies of Satan, the would-be usurper of God's rightful sovereignty.
Fortunately, the Bible charts from the start of Satan's strategy to steal from God that which is rightfully God's, through thousands of years of history of God's dealings with sinners, to his crushing of Satan and his followers, to judge the accuser. God's long-term plan to deal with this ancient rebel involves great spans of time because this issue is so utterly foundational to all creation and its Creator, it must be proven to all creation that God's judgment and punishment of this satanic rebel is utterly righteous. Then, nobody again will ever challenge God's sovereignty, for the eternal smoke of the torment of Satan and his hordes will simply be pointed to as the righteous fate of such rebellion and resistance to God's sovereignty (Rev. 19:1-2).
It would take a book to detail all of this progression through scripture, for it starts in Genesis 3:15 (showing God foreknew what would happen in Eden and had his plan of restoration already worked out.) It ends in Revelation 22:20 with the new heaven and the new earth in which righteousness dwells, God over all.
However, to give one example of what I mean, and to show that this is not merely my opinion, let me quote from a 614-page book that gives exposition of such matters by opening up the entire book of Revelation. This last book of the Bible is one of the best for showing God's sovereignty has never been overturned, nor have his rights to be God over all his creation been relinquished by him. Everything is under his sovereign control. Here is what it says about Satan and the mystical 'woman' who is depicted symbolically as both a harlot, and a city (Rev. ch. 17):
"The whoredom of the woman is spiritual, invisible, and indiscernible
to the world, because it is hidden in a mystery, so that the kings,
the great men, and the rulers of the earth are oblivious to the harlot
Babylon, and to the concept which this mysterious figure embodies...
The fornication of that concept of the Devil, and Satan, mystically
figured as a woman, consists in her revolt against the Creator so as
to unite herself with all that has been created and made, in whoredom
against him who made it. Thus she usurps the fallen creation, using
all the substance, riches and resources of the earth to seduce fallen
mankind to seek and live for such things in flagrant harlotry against
both the Creator, and the purpose for which all things were created
Thus the whore signifies the usurping of the creation itself -
consequent upon the fall of man in Adam - so as to evolve a system
utilizing the riches and resources of the whole earth in order to
entangle mankind by covetousness, thereby perpetuating the authority
and rule of the prince of darkness." The Revelation of Jesus Christ,
pp. 461-2, John Metcalfe, 1998 http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm
This book shows how Satan's 'beastly' system was dealt a deadly wound at Golgotha, when Christ defeated sin, death and Satan by his death and resurrection. At that point, Satan and his followers were cast down to Earth with no more access to heaven, to be "the accuser of the brethren". Satan is cast into an abyss, only allowed out for "a little season" to deceive the nations once more, before Christ suddenly comes to usher in the Day of Resurrection and Judgment. At all times, God is sovereignly in control, allowing evil to do its damndest, yet preventing it succeeding because he IS Sovereign over all creation! Those who doubt that are fair game for the great deceiver, who tries to usurp God's sovereign rights. Waken up to the tricks of Satan, and you will see that there is no question about God's sovereignty.
Make that your starting point for seeing why Christ did not deny Satan's claimed authority over the nations. Yes, Satan deceptively claimed to have all that authority, but he could only do so because God had granted him time to try to prove that his claim was legitimate, instead of being illegal. Because of the righteousness of God, the kingdom of God will triumph over this would-be-usurper, having allowed him all necessary time to try to prove his claim. No wonder Jesus said, "Seek first the kingdom of God and his righteousness, and all these things will be added unto you" - Matthew 6:33.
Alas for all who are lured into the kingdom of Satan - depicted symbolically by Babylon the Great, the whore, that is also Babylon the Great, the city. That is Satan's domain, granted to him by God to control, for a season. But only those who enter into the kingdom of the Sovereign God by the faith of Jesus Christ the King will "see" the reality of the deceptions of the would-be-usurper.