Bad people hurt others. They get hurt in return as a natural course of things. This is definitely not punishment if there is no God.
And if there is? They may face the direct or indirect consequences of their actions, but consequences are not necessarily punitive.
Many of these consequences are avoidable, so can we truly call them punishment anyway?
Suppose I am hated for abusing my cats. The hate is not punishment for my action is not making them hate me. It gives an excuse. Calling such reactions “consequences” risks sneaking punishment and blame in through the back door. It unfairly shifts responsibility onto the person being hated, making the idea of punishment itself seem hateful.
Hate is probably the most feared "consequence" if you do harm. Hate involves bad feeling towards somebody with a willingness to hurt them or wishing that fate would harm them. It does not require reciprocity or vulnerability in the same way love does. Hate involves a level of objectification of the person, and that is exactly why it can persist even when the other is unaffected or unreachable. Hate then is degrading. The one who hates you is doing wrong. It is a new evil. It is thus not a real result of the evil you have done. Once you understand this, you see that if you think your facing bad consequences for doing evil is going to deter you, then you are wrong.
Suppose there is a God who punishes sin. Or who sets sin up so that it punishes itself. Or who guides and authorises the state to punish me - meaning he is the real punisher. Then the punishment originates with God. To be genuinely helpful rather than judgmental, we must avoid claiming that people are being punished when in fact they are not.
We should not need to involve a God in this. Doing that smacks of using him as a crutch because we feel guilty about punishing or somehow unsure if we are fair.
We should also be cautious about offering comfort on behalf of God. Saying, “God loves you; you suffer so much, but it is not punishment” can sound glib—and who are we to speak for God? Such words may not comfort anyone; at best, they risk sounding foolish to those in need. And they imply God is sending discipline - that is not far from saying it is their own fault.
We conclude that the idea of bad results being connected to the evil you do, joined by God, is not very relevant.