How does being a net exporter even help? There's a global market and prices rise globally. US companies and consumers will pay more no matter if we're importing or exporting.
Most are public so my 401k gains. Oil companies will expand in this scenario and those new employees pay taxes, both which benefit everyone in some way.
I drive an EV so I gain. Though most lose more than they gain, this isn't a complete loss for anyone.
Why would an increase in oil prices translate to new jobs? The price increase has no relation to value added, only to global scarcity, so there's no need for new jobs.
The price increase, and the anticipation of the price increase, means that if you have the ability to produce oil, now would be a great time to be drilling wells. Of course, you have to consider the late time between how long it takes to drill a well and get production versus how long you think this will go on. Still, it's a reasonable investment that the oil business should be looking at right now.
This is where tariffs help actually, if they could be approved. You bring in money from tariffs, use that to subsidize things - gas tax is one way but it is small, but there could be others. Of course no tariff on gas exports since everyone wants it :) But it needs Trump world view with Obama's level execution :)