In a properly designed plumbing drain and vent system ... When the washing machine pump came on, his kitchen sink would gurgle and the water in the trap under the sink would be sucked dry.

The sink deck air-vent waste water discharging you describe ... The waste water is under pressure from the pump because the waste water must to be pumped up to the drain line under the sink.

Depending on the design of your sink, it may have one, two or three holes, and they may appear between the faucet valves, facing toward you, or under the ... has an overflow vent hole, too ...