It is impossible to ascertain the effectiveness and true output of an ozonator from a picture and a descriiption, particularly from a descriiption as vague as this one.
According to the scientists, the half-life of ozone in water is twenty minutes. That means that in twenty minutes, half of the ozone is gone or recombined into stable, bonded O2. You are correct. For this reason ozonated water should always be drank freshly ozonated for maximum benefit.
If you have not experienced any negative effects from the excess ozone in your room while ozonating water, if I were you I would continue as you have been doing. If you are experiencing shortness of breath, pain in chest, uncontrollable cough or headache you're getting too much ozone and should increase the ventilation factor. IMHO these symptoms are temporary and an indication of the body's need to detoxify. Ozone severely challenges the body to eliminate toxins quickly and this causes the cleansing reactions I mentioned.