Your statement is redundant. Atonement, or at-one-ment is being united (at one) with Christ. We become united to Christ when the Holy Spirit applies his life, death and resurrection to us, and we therefore die and rise in him. Our death in Christ is where our sin is done away with. Read the below passage from Romans 6:
Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? 4 Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. 5 For if we have become united with Him in the likeness of His death, certainly we shall also be in the likeness of His resurrection, 6 knowing this, that our old self was crucified with Him, in order that our body of sin might be done away with, so that we would no longer be slaves to sin; 7 for he who has died is freed from sin.
8 Now if we have died with Christ, we believe that we shall also live with Him, 9 knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him.
Substitution is nowhere in here. We need to die, with and in Christ. This happens through repentance when we become Christians, and when we physically die at the end of our lives. If Jesus died in our place for our sins as our substitute, then we should never physically die.