I have just been doing an exegesis in the book of Romans where I have been looking at Abraham's faith, which was accounted as righteousness before God. This means that Abraham was saved through His faith and obedience to God, thousands of years before Christ died on the cross. I believe that God gave him the title deed of his salvation, which was made real the moment that Jesus was raised from the dead.
This would be the same for the people who believed on Jesus during His earthly ministry. They were believing on Him in the Hope that they would be saved when He came into His kingdom. Remember the thief on the cross beside Jesus who asked Him to remember him when He came into His kingdom. Jesus told him that this very day he would be with Him in Paradise. Jesus could say that because the faith of the thief counted him as righteous before God in the same way that Abraham's faith was counted as righteousness.
All the saints of the OT testament who believed on God, were looking for and hoping in the Messiah for their ultimate salvation. Their salvation came into force as soon as Jesus was risen from the dead. As soon as the resurrection took place, God was able to legally justify those who believed in Him, from the very first person in the world, to the person who died believing in the last few seconds before the resurrection.
After the resurrection of Christ, then people accepted Christ as saviour, basing their faith and hope and the now finished work of Christ on the cross and His resurrection. Paul said that if Jesus had not risen from the dead, no one would have been saved (1Corinthians15), therefore the resurrection of Christ is the act that saves people who believe on Christ.
Therefore the OT believers were looking forward to the Messiah and basing their faith and hope on a future event which they believed was going to happen one day.
NT believers are basing their hope and faith on an event that happened 2000 years ago, and look forward to that they when they will be raised into newness of life at the Second Coming of Christ - an event in the future that we look forward to with strong hope.
The OT believers who now are aware of what Jesus did on the cross are awaiting the Second Coming as well when they will be raised up in newness of life to be with the Lord in glory.