Why are the ions produced
by Air Oasis safer than ozone?

The answer is really quite simple.  Is all due to the oxidation defense system, within your body, which utilizes a special blend of enzymes. 
Have you ever cut yourself on accident and then used hydrogen peroxide on the wound? What happened? The hydrogen peroxide started to fizz or bubble when it made contact with your wound, right? But why? It's due to the reaction of certain enzymes within our body that protect us from hydro peroxide, ozone, hydroxyls, super oxides and more.
One example is Glutathione peroxidase. It is a peroxidase found in humans, which contains selenocysteine. It uses glutathione as a electron donor and is active with both hydrogen peroxide and organic hydroperoxide substrates. Another enzyme is Catalase. Present in the peroxisomes of nearly all aerobic cells, it serves to protect the cell from the toxic effects of hydrogen peroxide by catalyzing its decomposition into molecular oxygen and water without the production of free radicals. Superoxide dismutase (CuZnSOD) catalyses the dismutation reaction of the toxic superoxide radical to molecular oxygen and hydrogen peroxide and thus forms a crucial part of the cellular antioxidant defense mechanism. 
Your body also contains many other antioxidants to help protect you from oxidation.  More and more of the foods we eat and the supplements we take are being loaded with antioxidants as well.

To put things in plain english; your body defends itself against these ions naturally, but mold, bacteria, viruses and other biological contaminents do not have the same defense mechanisms that we posses.  Therefore the ions we produce are deadly to simply organism, but won't harm people or their pets.