How does the aquarius calculate the correct amount of ozone for a given tank?
Apart from observing the physical effects on livestock, the only way to make sure that ozone is improving water quality is to use a redox potential meter. All other means are unreliable.

What redox level should the aquarist aim for?
Many fish-only tanks will be fine at reading of 250-350 mv. Sensitive invertebrates are best between 350-450 mv, but no livestock should be kept at levels approaching or exceeding 500 mv.
How can the hobbyist tell if ozone is in the main tank water?
By testing with a residual ozone kit available from a well-stocked aquarium retailer.
What are the effects of a residual ozone livestock?
It damages the gills of fish causing them to flick, scratch and breathe heavily. Death occurs in severe cases. Coral invertebrates will fail ti display properly for long periods and, like crustaceans, can die for no apparent reason.