I am not sure this is working the way it is intended so I am reporting it for you to verify.

The first  screen snapshot below shows that the level of crime at Ceres III is 23%.  It also shows the components that make up that total.  At this point I have NOT assigned a leader to the Minister of Justice position.

I then assigned a leader with 8 Diligence to the Minister of Justice position.

The second screen snapshot below shows that the level of crime at Ceres III has dropped to 2.50%.  All of the crime from the non-core worlds associated with Ceres III has disappeared and an additional 8% reduction has been added from my civ (Stink Lovers).

This implies that the 8% crime reduction from the leader in the Minister of Justice position applies to ALL worlds, both core and non-core.  Is this how you intended it to work or was it only supposed to apply to core worlds?