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.
Should you place it before the pressure tank then the filter will not automatically backwash.
If you have iron rich water with high hardness levels your system should be set up with the iron filter after 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.
As a softener also backwashes any debris and sediment making its way through will be flushed away during backwash while at the same time expanding the space between the resin beads to increase brine contact.
Why you may want a post filter after your water softener.
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.
Here is a diagram that illustrates how such an installation might look.
Each filter will need a particular pressure and flow rate to function optimally.
Fortunately captive air pressure tanks fill and empty through the bottom so little or no iron sludge will collect in the pressure tank.
Why you might need a sediment pre filter before your water softener.