Postmillennialists do not believe that God simply quits the historical battle with Satan, bringing time to an abrupt end. Nor do they believe that God defeats Satan in history by naked force. Postmillennialists believe that Satan's plan to spoil God's image by lies is defeated by the truth of the cross and resurrection. Satan's lies must be defeated by God's words of truth, and not sheer brute power, or else the message of history is nothing more than a demonstration that God is bigger and stronger than Satan.
Postmillennial hope is an aspect of Biblical soteriology.
In the Bible, soteriology and eschatology are one. Furthermore, the historical conflict between Christ and Satan is at the very heart of Biblical soteriology. That promise said nothing specifically of salvation by faith or of a future resurrection, yet the defeat of Satan meant the reversal of Satan's program and the undoing of all the damage he had done. The rest of the promises in the Bible fill out the meaning of the promise that Satan would be defeated. We must view the defeat of Satan and the plan of salvation through the Gospel as one, for that is the perspective of the Bible.