> Uphill. Water soaks into the ground and flows within it, on top of the bedrock which is impermeable. When the terrain allows it can emerge from the surface lower down as a spring.

This is one means of creating a spring, but not the only one.

Another means is an artesian spring, where water pressure inside the rock can force water upward a short distance. The ultimate source of energy is still gravity (the source of the pressure is water higher up trying to force its way down), but the water doesn't flow exclusively downhill.