The Old Testament believers had their sins forgiven just as much as us, through Christ alone. Although they lived in the time of ceremonial offerings, by faith they were under the promise given to Abraham hundreds of years before. That promise, as Paul argues in Galatians, was not invalidated by the law that came after it. So although they were under obligation to go through the motions of offering sacrifices according to the law, their status from the perspective of heaven was based on the promise, and that was guaranteed by the future perfect sacrifice of Christ.
What is it to redeem the sins rather than, as normally, the sinner? Christ had to buy out the sins – another way of looking at the atonement. He had to make those sins his own. He had to satisfy the justice of God concerning the existence of those sins, and cause them to effectively no longer exist in the government of God. Of course the fact that he has done this will be eternally remembered, for eternally his redemption will be the evidence of his infinite grace to his people.