Unless it is a storage field, the salt dome itself is solid salt, from the Jurassic Louann formation, that became semi-plastic under the load of all the sediment above, and bubbled up towards the surface because halite is lighter than most rock material. The oil is trapped in wedges of sand, that had been deposited nearly horizontally, but are pushed upright by the rising salt diapir. The salt is not permeable, and the oil, being lighter than water, migrates to the highest point, against the edge of the salt.
Sometimes salt domes are hollowed out by injection fresh water to create caverns, which can then be filled with natural gas, charged during the warmer summer months when gas is surplus, and drawn back down when gas is in demand, in the winter.
Or an old abandoned well could have developed a leak of water which dissolved the salt, or even a city water line might have leaked and begun dissolving salt.
