So I only had a short time to test last night, unfortunately. Just as I was about to start the stream, my X55 stick tension spring on rudder decided to snap =/
What I was able to test so far: Warzone kills last night, while I was sided with the Mining Corporation, did not provide any increase in rep this time, nor did they provide any increase in rep upon turning in war bonds. During the time I had to play, no Warzone missions for the Mining Corporation were offered, however there was a mission offered by Mining Corporation to kill 2 traders in a neighboring anarchy system. I traveled to said anarchy system, visited first USS I saw, and mission updated for alternate option via NPC dialogue (don't kill traders). I opted to instead kill the traders from the original mission offer. I did so, got mission complete dialogue, and at that point received no rep change. I then flew back to Mencke Orbital in Sorbago (where the mission was offered) turned in the mission, and immediately got negative reputation with Empire and the Mining Corporation instead of positive.
Is this a bug with reputation system itself, or are there typos / incorrect labels of the Faction that appears to be offering you the mission? Worth noting: all I received was the negative reputation for Empire and the Mining Corporation. I received no positive rep for any of the opposing factions in system. This is backwards from the expected, as I just successfully completed the original mission offered by the Mining Corporation, which is aligned with Empire.
Will test more tonight.