Imagine I have a plastic bottle filled most of the way with water and with a bicycle pump attached to the top without any leaks... If I increased the air pressure in the top of the bottle to, say, 30 psi (2 atm), how would that affect the water pressure below it? Now that the air above is at 2 atm, does that mean the hydrostatic pressure of the water is 2 atm as well?
The hydrostatic pressure at the bottom of the bottle will be increased by the amount of air pressure at the top that is in excess of ambient air pressure. Another way to look at it is that the weight of the water itself will produce an amount of pressure proportional to the height of the water column, and whatever air pressure there is above the water will simply add to the pressure due to the water column. So, the pressure at the bottom will be somewhat greater than 2 atmospheres.