You're making a very simple mistake.
Annorax did not represent nor work for any "Local" Krenim Imperium, and the "Locals" did not work for Annorax.
Two entirely separate entities.
When Annorax "changed" the universe, the new Krenim Imperium has no preestablished causal relationship with anyone who is temporally shielded. It's just a question of if the Local Krenim had met the local Voyager crew who might be near by causing a stink or half away across the galaxy.