Your conclusion is correct. There is additional detail provided in Revelation 20:7-10 that explain the timing between the 1,000 reign of Christ and the destruction of Satan. 

“And when the thousand years are expired, Satan shall be loosed out of his prison and shall go out to deceive the nations which are in the four quarters of the earth, Gog and Magog, to gather them together to battle: the number of whom is as the sand of the sea. And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven and devoured them. And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.” 

Verse 3 tells us that Satan’s release will be for only a “little season.” This time will constitute the final testing of mankind. Verse 8 suggests that Satan will have some success and there will be those who foolishly follow his lead. However, at some point, they will be destroyed in, what is termed in verse 6, “second death.”  
Verse 10 then tells us that Satan himself will be destroyed. This will be the end of death. From this point forward, death will no longer be known but will remain in the memory of all. God’s plan will have accomplished its goal of creating a perfect race, fully educated in the consequences of sin and the blessings of knowing God. 
What a delightful prospect!