The formula uses PoO in REAL time, but I suggest that the products react with time lag.
How long it takes the pig to work its way through the python on the way to the consumer certainly does vary. But that doesn't matter for the refining business, only for the retail gas station business.
Many (most?) refiners hedge their refining margins by locking in crack spreads, often at the time they settle on the price for the oil purchase even though it will take weeks for ship delivery. Refiners are major sellers of products in the futures market, offset with oil purchases. Then they unwind the trades as they ship physical product. They also trade crack spread contracts for the same purpose. Unlike producers, hedges usually only go 2-3 months max into the future, and are based on commodities already physically present in the market. But there could be speculators who go further, particularly when crack spreads are really attractive.