Oil power plants are only refueled by trucks carrying “Oil Products” from specialized industry (or imported from off the map). They are never refueled by trucks carrying “Oil” or “Petroleum” which is created by Industries DLC buildings.
It is extremely easy to test this. Make a new city with unlimited funds, unlimited resources, and everything unlocked. Get some Cims to move in, then make two separate test areas with access to oil resources. Put an oil power plant and an incinerator (not a recycler) in both of these areas. Disconnect them from the rest of your road network to make it an easier test, but it is ok to put in some path connections so that your cims can walk to work.
In the first test area paint a district, specialize it for oil, and then zone some industry. Put in a warehouse that holds “Zoned Industry — Oil Products”.
In the second test area paint an industry area, build the oil industry main building in it, as well as a large oil pump, an oil storage building, one of the petroleum plants, and a warehouse set to store Petroleum.
Both power plants will start out with enough fuel to run for a couple of months. During these months your warehouses should begin to fill up, but because the roads are disconnected they will only fill up with what you are producing locally; there will be no imports.
As you continue to run the game, watch which power plant gets refueled and which runs out. You’ll see that the one in the oil industry area will run out, while the one connected to your specialized zoned industry will not.
I assume that the same is true for coal and nuclear plants; they will be refueled by “Ore Products” from specialized ore industry but not refueled by any resource produced by Industries DLC ore buildings. I’ve never tested it though.
Since traffic problems can prevent fuel deliveries from making it on time, I recommend having a warehouse holding the appropriate products set to balanced near your power plants; deliveries from this warehouse will be much quicker than imports from the edge of the map and traffic problems will be less likely to have a major effect. I also recommend using wind, solar, and hydro power whenever possible simply because they are not prone to refueling problems.