Having read widely the accounts of near-death experiencers and the works attributed to the deceased (who are said to have spoken and dictated books through mediums) it becomes clear that there are 2 main processes at work to achieve the justice that is described in Romans 12:19:
Do not take revenge, my dear friends, but leave room for God's wrath, for it is written: "It is mine to avenge; I will repay," says the Lord. [NIV]
These 2 processes are self-judgement as part of the life review process that seems to occur amongst the recent deceased. The other process is the balancing of karma that seems to be required in future lives for our past deeds. This "balancing of karma" is the process whereby we experience in our own life the quality of experience we caused another to experience in a previous life. So, for example, the person who forcibly puts another to death against their will will experience something similar where their own life is forcibly taken away by another.
The life review process is one that is commonly reported by near-death experiencers and the recently deceased. They describe it as a process where they experience all, or the most important moments of their life, in vivid detail and experience how they were feeling at the time along with how all other people involved were feeling. In this way they get to experience how other people responded to their actions and what this means for the wisdom or otherwise of what they put into motion. This helps to enlighten the soul to their tendencies and helps them to amend the unhelpful ones moving forward.
As can be seen, these two processes are the works of a loving God who seeks our clarification and wisdom moving forward rather than some kind of blind punishment for wrongdoing.