This could cause a problem with the expanding and collapsing magnet field of the solenoid. The HES switches based on a change in the magnetic field (once the proper amount of magnetic field is sensed) rather than the strength of the magnetic field at any given switch point.
When you fire the emag, the solenoid magnetic field expands or collapses around the HES. Normally, this doesn't affect the operation because the program only senses the pull of the magnet into the HES, and the magnetic field fluctuation is ignored because it is back to normal in time for the next trigger pull. In any firmware version that allows a trigger capture before the solenoid completely resets can be affected by the changing solenoid magnetic field because it can oppose or add to the existing magnetic affect from the trigger. This can cause the HES to go through the on-off range without actually moving the trigger.
In your self calibrating HES, the same issue could occur. If you pull the trigger and activate the HES, the firing of the solenoid will affect the magnetic field around the HES, causing it to be in the changing magnet field. It won't be biased by a permanently installed magnet, so that won't be an issue. Only the changing magnetic field will affect the operation. If you are running firmware that ignores any switch inputs during the solenoid magnetic fluctuation times, then only the initial magnetic value will determine the firing point. After that, only the final position(s) of the trigger, before any change in direction, will be evaluated. The trigger will essentially activate and reset based on movement distance rather than passing a fixed point. A problem might present itself with the changing magnetic field in any firmware where the trigger event can be captured while the solenoid is active. The active solenoid will cause the magnetic field around the HES to change which could simulate a magnetic change equivalent to a reset and pull of the trigger, even though no physical movement of the trigger has occurred.
So, in a nutshell, your HES might work fine for most emag applications. If it is firing properly, without going full auto, then you are probably fine. In fact, it might actually work better, as you have indicated based on your response. You should be aware that it might make an existing known problem worst for some firmware versions. Note: We can correct the known issues by using a capacitor of a known value on the trigger input. I don't think we will be able to do that correction on your HES because it is a hysteresis issue and not a rapid impulse caused by a changing magnetic field.
Except for the Automag in front, its usually the man behind the equipment that counts.