It can't equalize to that lower pressure because of the limited volume of the tent.
the air in the cylinder has a lower oxygen content than the air in the tent, but is at a higher pressure, because you are at altitude. when you open the cylinder, the 15%-oxygen air from the cylinder mixes with the 21%-oxygen air in the tent and both the oxygen content and the pressure equalise. this has nothing to do with the volume of your tent.
the effect of this will be that you are breathing air that is lower in oxygen content than the air at altitude, and it is also at a lower pressure than the air at sea level. this is therefore worse than getting altitude sickness.
cheers.