Does this mean that if I commit a crime in the neighboring forum, I can get punishment here?
If you are tagged for a proven scam that was done on the other forum then you will be affected. But if someone tags you for trolling, personal dis-likeness or anything else that happen on the other forum which is clearly not a good reason to tag on this forum then I don't think the tag will matter at all.
There's more things on teleporting than we see. If a username is teleported, also reputation is teleported
You summed it up very well here. It's vice versa too. So I must say that protect your account on the other forum too so that anything bad does not affect you on this forum too.