The adsorbent beds of a pressure swing adsorption (PSA) column are capable of removing water vapor down to a few ppm. That water accumulates on the adsorbent during the production stage of the PSA cycle as ambient air is fed to the column, nitrogen and the other non-oxygen components are adsorbed, and concentrated oxygen is produced. That cycle continues until some of the non-oxygen constituents show up in the product. When that happens the pressure in the column is released by allowing gas to escape from the inlet end of the column. This reduction in pressure causes the bulk of the adsorbed non-oxygen gases (including the water vapor) to desorb from the adsorbent so that its adsorption capacity is restored. When that is completed the column is repressurized with air again and concentrated oxygen is again produced. A system will commonly contain 2 or more adsorbent columns if a continuous flow of product oxygen is needed (so that one column is always producing oxygen while the other(s) are in regeneration). A single column design can also produce product continuously by feeding the product oxygen to a pressurized holding tank from which oxygen may be drawn even when the adsorbent column is in regeneration and not producing oxygen. A single column system can also appear to be operating continuously if the cycles are run for very brief times (pulses) such that the saturation point is kept within the bed and simply shifts back and forth a short distance between cycles (pulses).
Even if the adsorbent did not remove water from the gases, product oxygen at 1500 psi is very dry simply as the result of its pressurization. At common ambient temperatures water condenses whenever the partial pressure of water vapor exceeds about 0.02 atmospheres (round numbers, warmer temperatures will make it higher and lower temperatures reduce it, but 0.02 atmospheres is close enough for this analysis). Worst case the air that is used to produce the oxygen is saturated with water vapor at 1 atmosphere total pressure (i.e., it contains about 0.02 atmosphere partial pressure of water vapor). The act of compressing that air up to 1500 psi increases its pressure by about 100x (1 atmosphere is about 15 psi). That means that the water vapor that was originally at 0.02 atmosphere partial pressure is now at 2 atmospheres (100 x 0.02). But anything above 0.02 atmospheres would condense as liquid water and be removed from the system by a blowdown valve or some other mechanism. The resulting compressed gas now only contains about 1% as much water vapor as it had initially (0.02/2). When the pressure of the gas is reduced from 1500 psi back down to 1 atmosphere or 15 psi (or less in an airplane) by the regulator, the partial pressure of water vapor, which was 0.02 atmosphere, is reduced 100x down to a very dry 0.0002 atmosphere.
Also, while compressed gas cools as it is depressurized, the rate of gas delivery in a typical airplane oxygen system is so low that heat transfer from the ambient environment warms it to ambient temperatures before it has a chance to freeze anything. That system that cools beer using a fire extinguisher is probably delivering hundreds of cubic feet of CO2 GAS per minute. That CO2 is also stored as a liquid in the fire extinguisher (CO2 liquifies when pressurized). So the adiabatic heat of vaporization also contributes to its cooling capability).
As for the humidistat only reading 16% humidity when purged with the systems oxygen, I expect that the meter is not designed to operate accurately down to the low moisture contents of that oxygen. It's not capable of indicating lower. Something like a chilled mirror sensor might work, but even then the dew point (actually the frost point) of the oxygen is probably so low that it might challenge the capability of the mirror cooling system to cool the mirror down to the condensation point of water in that gas.
The oxygen produced by the OPs system will work just fine in the plane presuming that he has a regulator that fits the bottle and is capable of delivering air at the prescribed rate into a varying ambient pressure. It might require that oxygen flows be bumped up about 10% compared to cyrogenic oxygen to compensate for the ca. 10% lower purity of system oxygen relative to cyrogenic oxygen (90% vs. 99%). But otherwise it will be fine.
