Interesting, I've never had that happen. Currently, both Empire and Millikan rep is increased when killing Cartel ships in neutral or IMC space, but Empire rep increases MUCH more slowly than Millikan rep decreases if you kill them in Millikan space, and vice-versa.
I figure this is a bit of an edge case given that it can only happen if you're close to allied with the Empire and decide to go pirate-hunting for Millikan (who you have much lower rep with), which is why it hadn't been found before - I'll try to include a fix in the next patch.
Thanks for the report, I genuinely wouldn't have found this otherwise!
Edit: Not 100% sure how this happened to you, I reviewed the code and it would appear that in Millikan space Empire rep is reduced by killing Cartel ships, as they don't appreciate you doing pirate hunting on their enemy's behalf. I'll double check whether or not there's a Millikan sector that's tagged incorrectly as a next step.
Edit 2: Looks like all the sectors are tagged correctly. I'll attempt to reproduce the issue and report back if I manage it.