Oil price does not directly reflect turbine fuel price. There is a "refiner's margin" that varies between $10-$40 dollars a barrel on top of the base oil price. Supposed to go towards the extra cost of actually producing avtur and it's higher quality etc.
It is also sometimes used as a profit enhancing tool, when refining capacity for the product is low, the "margin" suddenly becomes higher.....
At oil's peak price of about $145 or so not long ago, turbine fuel was $185 per barrel.