What I can say is that the system "works" if you lower the Pools, the production and increase consumption of Divisions (just to see if it works at all). But it seems like the amount of Production, Military consumption and Civilian consumption need to be in a specific ratio for the system to work.
The thing is that
someone, while the whole Axis is "afk", is reducing the Pools by ~-75k. This means that this
someone consumes 75k+~85k+~55k=215k per turn.
To put this into perspective:
Had the Axis 100 Tank Divisions and would expend all their fuel each week, it would consume ~500tons x 100 Div = 50k.
Would the Axis fly 5000 Sorties each week and assuming an average Fuel per Sortie of 2ton (Fighters use ~0.33tons) we would only consume 5000 sorties x 2 ton = 10k fuel.
Then there is some fuel supposed to be used for Supply Trucks.
All in all, the numbers actually consumed "on MAP" in these 3 positions to me seem rather miniscule, like the 100 Tank Divisions are an extreme example already.
In whatever way the Supply system may actually work/in which order the Fuel is actually delivered, ...even if a little bit is left in the Pools after civilian consumption, this rest seems likely to meet/exceed the consumption of what your Ground Forces and Air need.
Attached an order of Logistics Phases (it's a while old not sure if some Phases have been moved since then).

- Fuel Issue_Logistics Order.png (197.72 KiB) Viewed 67 times
My assumption is, that after the Civilian Phase (which uses the Fuel from the previous Production [which may only have been consumed/"touched" so far from stuff consumed during Air Phase]), there must be sufficient Fuel inside the Pools left to fully support Ground+Air. So this means somehow the ~-215k consumers (during Axis afk) stop consuming that much when Fuel gets low and Forces will (before also Rumania falls and Pools are drained) have sufficent to fill their Tanks.
If one would now balance it in a way as to have ~85% of Fuel needed for Units each turn, the issue would be that you likely would have no way of stockpiling Fuel in preparation of an offensive, since (I assume) the
someones which like to consume ~215k but then reduce that to X would likely increase consumption again.
How did this work in WITE1+WITW?!