Good premise for a fiction!

So, there's a totally different Earth timeline from 4000 BCE? OK, so is the question what happens in 3990 BCE once people may have figured out the rules? If not, when? (and in the alternative time period what is society like?) Also - where? - very different situation on a small Pacific island compared to a large land mass. Question is both too broad and too undefined currently.

why punish rehabilitation works better.

Considered in detail in The Stars My Destination by Alfred Bester, 1956. Rather than write a long paraphrase and analysis, I'd recommend you just read it. Lots of clever solutions (and problems) in it. Also, if your story involves non-technological teleportation, you want to be familiar with this famous work since yours will undoubtedly be compared and contrasted.

@John so how would you rehabilitate them? I think such a frame challenge is very acceptable.

I have to say, we use prisons as a form of punishment in quite recent times. Before then, for the course of the history the most popular punishments were corporal ones, aside with fines, mutilations, and executions.

There might be some solutions based on how they teleport. For example, if their molecules are moving through space, there may be some matter that can stop this. If they create some sort of wormhole, you may be able to distort this. If they need to "charge up" beforehand, you may be able to detect and/or stop that. Etc.

More on Besters' The Stars My Destination: I wrote a blog article (in context of its influence on D&D) at the following link. In particular, check the bullet on Ch. 5 and the Gouffre Martel (prison in the French Pyrenes): deltasdnd.blogspot.com/2018/08/teleport-traditions.html

I'd also add that prisons would lose a lot of their appeal once every criminal that has ever been there can just teleport back and give his mates/clients stuff. It's easier to just revert to corporal and financial punishments than to go to the hassle of detaining people for periods of time.

Also note that it would be much harder to murder someone if the victim can easily teleport.

You'd need the element of suprise

Sorry if I've missed something, but how do you catch someone to punish them?

Vernor Vnge's novel The Witling concerns a culture that has psychic teleportation. I don't remember what he said specifically about preventing criminals from escaping punishment, but it's Vinge, so he probably thought it through.

After the previously mentioned The Stars My Destination and The Witling, there is also Jumper by Steven Gould. They all cover many, many considerations of teleporting. Even though he deals with mechanical tech teleportation, Larry Niven also put a lot of thought on what it would do to society.

I was going to mention Alfred Besters The Stars My Destination, but was beat to it. In it is found the most elegant prison for anyone who teleports. Must read fiction regardless.

@MathCookie Most stars have a much larger volume than Earth and all stars are at least thousands of timess as massive as Earth, so Earth would land on a small blue star instead of vice versa. And Earth would be destroyed as it collided with the star. So maybe you should think of some other type of astronomical object influencing people on Earth.

Question 1: "5 times their weight" Do they get to choose? IE: If you stun them with a stun gun and then wrap them in chains or chain them to the ground? or do they just poof out of restraints?

Final question: Can electronics attached detect the teleport? Something like Cartmans V-Chip and the "don't do that" zap? You can pair the GPS with a V-Chip to punish the baddies by geo-locking them and knocking them out if they leave an area if so

@John Because we're still dealing with humans whose psychologies are notoriously unoptimized. Nothing about this scenario makes punishment and revenge less likely to be the reaction of choice; just harder to implement.

"they can teleport with them 5 times their weight" is this by choice? I mean they choose what can teleport with them or when they teleport they automatically take with them everythig they're touching up to 5 times their weight? how do this work with clothes and equipment?