Oil floats on water, which means pumping water into the bottom of the cavern pushes the oil out. As fresh water is pumped into the bottom of the cavern, the oil gets displaced upwards into a delivery system.
The more water you pump in, the lower the quality of the oil that's pumped out; we are basically loaning the oil refiners money to buy SPR oil they don't really want. Also, the more water we pump in, the more salt leeches into the water and the more the bottom of the chamber deforms, creating shear forces in the upp walls that lower its overall structural integrity.
I've posted this before; it's a recent report on the status and maintenance of SPR facilities, which is very clearly written and well worth your time if you want to understand the topic better: https://www.gao.gov/products/gao-26-106918