"For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people." (Hebrews 10: 30)
When we read this passage, context is important.
Here, the writer of Hebrews is commenting on the finality of Jesus' death on the Cross, and that there will be no mercy for those who reject it.
To this day, there are many Christians who do not believe that Jesus has finished the work of putting away our sins forever and bringing us into eternal life.
Usually, it is the second part which they fail to receive.
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." (John 3: 16)
We face death because of our sin ("The wages of sin is death" (Romans 6: 23), but Jesus died for us and as us, delivering us from both:
"4Wherefore, my brethren, ye also are become dead to the law by the body of Christ; that ye should be married to another, even to him who is raised from the dead, that we should bring forth fruit unto God. 5For when we were in the flesh, the motions of sins, which were by the law, did work in our members to bring forth fruit unto death. 6But now we are delivered from the law, that being dead wherein we were held; that we should serve in newness of spirit, and not in the oldness of the letter." (Romans 7: 4-6)
Regarding judgment of His people, let us remember that God has judged all our sins in the body of His Son:
"For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:" (1 Peter 3: 18)
This vengeance which God sought for Adam's sin, He found in the perfect sacrifice of His Son:
"He hath not dealt with us after our sins; nor rewarded us according to our iniquities." (Psalm 103: 10)
"23For all have sinned, and come short of the glory of God; 24Being justified freely by his grace through the redemption that is in Christ Jesus: 25Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God." (Romans 3: 23-25)
"In whom we have redemption through his blood, even the forgiveness of sins:" (Colossians 1: 14)
In Christ, we have redemption from all sins, and God is avenged for our sins through His Son.