The only reason I can imagine for a specific tax on California oil producers is the apparent belief by the proponents of the tax that these costs will be borne not by California drivers but instead by big oil companies. One of the most curious features of the Act is Section 42004(c):
The assessment imposed by this part shall not be passed on to consumers through higher prices for oil, gasoline, or diesel fuel. At the request of the authority, the board shall investigate whether a producer, first purchaser, or subsequent purchaser has attempted to gouge consumers by using the assessment as a pretext to materially raise the price of oil, gasoline, or diesel fuel.
The standard explanation economists give for why a tax like this would of course raise the price to consumers is that it will cause the least profitable California oil reserves not to be extracted. With less supply, the price has to rise. This is not a conscious decision of anybody to "pass on" a cost or "gouge" a buyer, but simply is the way that markets work. The designers of this legislation evidently recognized this as a potential concern, and decided simply to rule out the natural and necessary market outcome with the stroke of a pen, leaving yet another job for judges to try to divine whatever California voters must have intended by terms like "pass on" or "gouge".
Growing up in L.A., I often heard jokes about what a bunch of nuts we Californians were. At the time, I didn't get the joke - the only status quo I ever knew seemed normal to me.
Unfortunately, now that I see more clearly, the joke's not funny anymore. Economic illiteracy is no laughing matter.