Been away from it long while, but not sure you have a conventional softener there. It does have a softener salt day tank?
A normal softener uses ion exchange in resin media. Calcium, magnesium, iron and manganese are exchanged with sodium. Periodically, the system backwashes the crud out, and rejuvenates the media with fresh sodium (softener salt). Iron is a challenge for a softener, since it can be a +2 or +3 ion - so 3 sodium +1 ions are needed for a single +3 iron.
This uses an ozone oxidation of the iron, in place of chlorination. Ozone (O3) is a strong oxidant. Changes oxidation state of the iron to make it easier to remove. I would occasionally recommend pellet chlorination directly into a well to help with iron under same principle - would precipitate some out in the well before it gets to the house.
Ozonation was a new technology years ago, so I didn't have much experience with it.
Where is the ozone injected into the water? Guessing it gets ozonated first, then goes through a conventional softener next, or other filter of sort?
Wondering if treatment time is too short between hitting it with ozone and the removal/filter/softener?
Or, your iron concentration such that it is not taking the iron out effectively, and it continues to (rust) in the piping after the treatment system?
Iron (red) and manganese (black) are pretty common 'round these parts. They can be a challenge to control without fancy chemical treatments, which I don't suggest either.
Keep tabs on your control adjustments, and see if it does improve. This system should do better than a regular softener.
I dealt with a village water system that used polyphosphate for Fe/Mn. ~200 gallons per minute were treated. Phosphate would bind (chelate) it up so it couldn't oxidate. Didn't work at first. Realized didn't have adequate mix/reaction time before it hit system turbulence, and would still turn brown. After moving treatment point further away - had more time, and worked.