Think of the quarry like a brand new reservoir, with the normal groundwater/spring elevation being the spillway elevation. When the quarry is filled to that elevation, water will flow normally via those springs (over the spillway if you will). But until it’s filled to that elevation, no water will flow downstream of it without pumps bypassing water around the quarry (or a manually operated bottom release gate in the case of a reservoir).
Just like a filling a reservoir, it takes time and surplus precipitation to fill the quarry. Ideally, if the quarry were to close, you’d continue to use the pumps to pump a minimally viable constant flow to the streambed to sustain fish life, while allowing any excess precipitation to refill the quarry. Once the quarry was full to the natural groundwater level, the springs will flow, the water table will behave normally, and you can shut off the pumps.