I have several sinks. When you speak about the air coming out...what comes to mind is that the rubber "seal" inside the sink's valve is either damaged or "out of place somehow. This has happened to me before. I think I just kept playing with airing it up and releasing the air. Hopefully you are not using a needle on the pump. You could try to suck out on the pump and then remove the pump and this may place the valve in the right location. The screw on type is the only way to go. As far as the amount of air ... you should place the component on the sink and inflate to where there there is 1/8" free movement when you squeeze each corner.
Jeff
Jeff