[Chaos]

What I mean is if a crime is committed in say...dormeho, imperial guards cannot arrest you in chaturanga, and chaturangan guards will not arrest them on behalf of the empire.

1. If a known criminal from Sigrogana tries to jump over to Chaturanga and go 'haha you can't arrest me here', it's highly unlikely that Chaturanga won't go after them, especially when it's very much possible for said criminal to repeat their offenses on their soil.
2. If Chaturanga didn't go after them, the Empire can put pressure on them. Not to mention the fallout that can come from harboring what would likely be a serious criminal, which is twice as bad for a nation that's focused on being neutral to the rest of the Great Six.

Imperial guards will not jump continents, but if you're expecting for the rest of the Great Six to completely ignore the crimes you did on another continent's soil, think again.

(No, this doesn't mean petty crimes are going to ruin you in every nation forever, nor is it completely impossible to slip out into another nation while keeping yourself out of trouble.)