Most iron in well water, is typically in a ferrous state. Ferrous iron is commonly called 'clear water iron' as the water remains clear as the iron is fully dissolved in the water.
Although ferrous iron can't be simply filtered out using a sediment filter, it will adhere to a softener's resin granules, thereby lowering the iron amount exiting from the softener while also reducing the resin's ability to remove hardness unless appropriate additional maintenance is regularly performed to remove iron accumulation from the resin (acid cleaning to prevent iron fouling).
As each 1ppm of ferrous iron will deplete the same softening capacity as removing 85 ppm hardness (5 grains per gallon), the hardness setting must be increased, resulting in more frequent regeneration cycles with a substantial increased amount of salt utilized each month/year. Removing ferrous iron with a softener is simply not an efficient method. Although not efficient, when the amount of ferrous iron is relatively low (typically ~1 ppm or less), sometimes a softener will be utilized for iron removal, to eliminate the additional expense for a dedicated iron removal system.
The Birm media within your iron filter, is intended to catalyze the ferrous iron, converting it to a ferric state, so the resulting solid rust particles that precipitate out from the water, can then be filtered out by the remaining Birm media located lower within the tank. During each Birm backwash cycle, the solid rust particles will be flushed out to drain.
While both Calcite and Birm have similar backwash flow rate requirements, (8-12 gpm/ft2 for Calcite, 10-12 gpm/ft2 for Birm), with mixing both medias within the same tank, the quantity and bed depth for each will be reduced and so neither media will perform as effectively as intended.
In addition, iron removal media will perform most effectively when pH is 7.0 or higher, so with the Birm and calcite mixed together, the pH is not being increased prior to the Birm media, so its effectiveness is further negatively impacted.
When an iron reduction filtration system is correctly configured and functioning properly, the softener should be removing little if any ferrous iron.