I could be wrong, but I think there is some "bleed" when you loot regions. Sympathy for your realm in adjacent regions (that belongs to the same realm that you're looting) decreases as well, although not nearly as quickly.
The mythical bleed.
I seem to remember devs saying it didn't exist. Besides, even if it does, it certainly doesn't have any impacts more than 1 region away, because Rio looted Enweil quite a few times over the years and yet the western regions still loved them.
