Each boss only counts once. It will count your highest difficulty for each boss. These kills are then ordered from highest difficulty to lowest to set the thresholds for each slot, very similarly to how the Mythic+ thresholds work.
So your list looks something like this for purposes of the vault, I’ve marked the 3rd and 7th positions:
Shriekwing - Heroic
Huntsman - Heroic
Hungering - Heroic
Council - Normal
Generals - Normal
Sludgefist - Normal
Inerva - LFR
You have 3 heroic kills, hitting the first threshold, so you get a 213 as your first choice.
You have 3 Normal kills, but this isn’t enough to get you to a 2nd item in the vault, as you’re now at 6 kills at normal or higher.
Inerva is the only LFR boss which was not also done on another difficulty. So it counts as your 7th boss and grants you a 2nd item, but it’s LFR, so that’s the level your 2nd item is set to.
Had you done exactly this, but then also done the other 3 bosses on LFR (which I’m aware is not possible at the moment), you’d have all 10 bosses and would have a 3rd slot open, which would also be offering an LFR piece.
Had you done Inerva on Normal as well as (or instead of) LFR, your 2nd item would be from the Normal pool.
It’s working exactly as intended, the presentation just seems to be a source of confusion for a lot of people.