In some senses, "The US" is not really involved in oil production. It is a more privatised industry in the US than most (oil producing) places. If oil prices go up in the Persian Gulf, petrol prices go up in Texas regardless of import/export balances.
In theory, the surplus profit is enjoyed by Texan oil producers, as opposed to Gulfy producers. This is increasingly dubious as the economy globalises. Gulfies own an interest in Texan oil wells. Texans own an interest in Gulf oil wells.
The Texan putting petrol in his ute... I'm not sure it matters to him that the US is a net exporter. Petrol costs him more. Oil derived products cost him more. His income does not increase.
This is not true in the reverse. In most oil producing nations, people do not pay the export price for oil. The local market price is usually lower.