Battlemage's Cry

Is there reason why Battlemage's cry can't trigger any spell supported by Archmage support gem? or is it a bug?

trying to be cheesy and get an elemental equilibrium proc and curse with BMC + arc + hextouch + frostbite but it doesn't curse with the arc. It does cast the arc and if i take out hextouch it can cast hex, but separately.

Am I missing something in the wording of the skill gems or does this not work in general?