Just because it is not mentioned does not mean that it is absent. Many things are IMPLIED in Scripture.
Here is what is said to the righteous ones: Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
We know that it was Jesus who said that the New Birth is imperative in order to see and enter into the Kingdom of God (John 3:3,5). And we also know from Scripture that it is by believing on the Lord Jesus Christ that sinners are born again (John 1:12,13). So it is implied that these on the right hand believed on the Lord Jesus Christ and had been born again.
Now here's something to work with, and thanks for the post. The real nuts and bolts here is trying to discern how and by what means they would come to recognize Christ as not only Lord, but
Savior, and it is clear from your quoted verse that they would have to at some point. But the interesting thing is that this event apparently happens after His return, since again, His judgment upon them isn't based upon their having believed in Him as Savior but for having helped those who did... One could say they believed after the rapture of the church, but this would become their justification. I think it suggests that justification by faith was there in their hearts all along for having chosen the good over the evil even when the church was still present. But it would take the return of the Lord and the establishment of His kingdom on earth before they made the determination to give their lives fully to Him, and have sought the forgiveness of their sins by the time they stood before Him...
Again, it goes back to the power of the conscience, and whether a man chooses to listen to it or not. Those guided by it will find their way to the Lord, to the truth, to salvation by grace, and to forgiveness. Those who don't never will.