Additionally if installed before the pressure tank there is a chance the water would flow backwards from the pressure and enter the iron filter control valve through the outlet pipe.
Iron filter before or after water softener.
Note that this installation includes a pre filter before the neutralizer.
Why you may want a post filter after your water softener.
If you have iron rich water with high hardness levels your system should be set up with the iron filter after the pressure tank.
Each filter will need a particular pressure and flow rate to function optimally.
The neutralizer should be installed before your iron filter and water softener.
Fortunately captive air pressure tanks fill and empty through the bottom so little or no iron sludge will collect in the pressure tank.
Since softeners are not designed to address undissolved iron and manganese a whole house particle filter is good solution for reducing and or eliminating insoluble iron and manganese.
Most iron filter medias will typically oxidize the clear iron and then filter out the solid particles which are then flushed to drain during the backwash cycle.
Why you might need a sediment pre filter before your water softener.
Again this particle filter can also serve as a barrier protecting your water softener conditioner from clogging and thus extending the life of your unit.
Although most water filter cartridges that are used as a pre filter are not fine enough to capture non dissolved iron in the water a 5 micron pre filter cartridge is fine enough to capture iron particles.