I think this is to aid and speed up acclimatisation while also reducing the risks.
The barracks would not be pumped to sea level oxygen levels to start with, so when the troops arrive, their bodies would start the acclimatisation process even while in the barracks.
You could then gradually reduce the added oxygen levels over time, and supplement that with ever increasing outdoors activities.
The analogy I can think of it’s interval training, where you alternate between sprinting and jogging to maximise your workout effects.
The soldiers would start going outside for exercises when they first arrive, but those would probably be limited in time and intensity to avoid putting the men in danger. They can then go back to the barracks to recover much quicker, and be ready to head out again fresh to train some more. With the duration and intensity of the outdoors activities gradually ramped up even as extra oxygen levels inside the barracks are reduced.
That is more akin to the high altitude training that elite athletes undergone, whereby science is employed to get troops accliaatisatised in the shortest time with the least risk possible, and should be significantly more efficient and effective than traditional methods, as that just allows you to gradually get used to the reducing oxygen levels without being able to do the intensive ‘sprint’ training of going out in actual full low oxygen conditions until you are at the deployment area itself.