The Axe pedal jacks wouldn't be causing any problem here.
First make sure the Midimate is on the preset you want to add pedal function for. Press "2nd", then press either "Edit Function Select" button a few times until "Controller Assignment" scrolls on the display. It will be let you change the Pedal CC # once you press either "Bank/Adjust" button. You can set it to any number--let's say 6 for this example. If you move the attached pedal, it should begin to show the values being sent out, hopefully ranging from 0 to 127. (My Roland pedal doesn't drop below 30 with the Midimate, which has no calibration function, and I only use it with the Axe pedal jack for this reason. It's good to check Midimate/pedal compatibility while it's easily done at this point.) Press 2nd to return to normal operation.
One thing I didn't mention before is the pedal's MIDI channel. When in editing mode, use the "Edit Function Select" buttons until you see "MIDI Channels", wait a few seconds, then continue using those buttons until you see "PEDC". Use the "Bank/Adjust" buttons to set it to match the Axe-FX MIDI channel, which is probably 1 if you haven't changed it in the Axe I/O menu.
Now go into the Axe I/O menu, CTRL page. Set any of the External (1-8) controllers to "6" as mentioned earlier. This is if you want to be free to assign the pedal to any modifiable parameter in an effect. So, if you set External 1 to "6" in the menu, you'd edit a block, hit Enter on the parameter you want to control with the pedal, then set "External 1" as the modifier.