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There is a shut-off switch (double-pole? I mean it's a switch that looks like a light switch but has 2 sets of 2 screws) next to the tank with the pump switch.
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Apparently, that shut-off switch doesn't shut off...

I think it's because the pressure switch was wired AHEAD of the shut-off switch, so it only kills power to the pump motor.

And, having grown up in a house with a well for water, you shouldn't mess with the pressure switch settings anyway. You may cause the pump to cycle too often or create an overpressure situation.

Adjusting the nut changes the cut-off pressure, the cut-in pressure is a fixed value below the cut-off pressure. (Usually between 7- 10 psi.)

MKD Steve has the best idea.

And to your original question, the breaker is most likely o.k. I've had a few "oops" situations where a momentary arc isn't enough to trip a working breaker. [Linked Image]

Stupid should be painful.