The most important thing is the VOLUME of air that your pump will produce not the PSI.
I assume that you your reservoir is lest than 5’ deep. At 5’ of water the pressure is less than 3 psi so anything over 3 psi will cause the air to bubble up through the solution.
(34’ of water =14.7 psi = 1 atmosphere of pressure, so divide the depth of your reservoir in feet into 34, then dived 14.7 psi by the number in the first step and that will give you the pressure in the bottom of your reservoir)
I agree that any air pump for a tank of at least twice the volume and preferably 3 times the reservoir capacity should be sufficient to aerate water and/or nutrient solution.
How many 12" air stones are you trying to run off of one pump and what is the tank size listed for the pump? If you have too many outlets i.e. to large and/or too many air stones running off of a small pump you will not see very many bubbles. Try disconnecting all but one air stone, see if you get good bubbles, if so begin to reconnect them one at a time until you aren't satisfied with the amount of bubbles you get. Then fall back to the number that worked, and that is the maximum number of that size of air stones you can run for that pump.
The options then are to either get a bigger pump or get additional pumps. I prefer to run at least 2 pumps of a capacity nearly large enough for the size of reservoir so that if one of them fails, the solution remains aerated. If is also a good idea to run them off of separate electrical circuits so that if a fuse blows or a circuit breaker trips, both pumps do NOT go off at the same time.
Good luck.
Don Jones