Right now it counts "kills earned by the soldier that occured on the hostile turn, where the weapon was not a grenade or a proximity grenade."
The problem is: when a unit bleeds (or burns) to death, game attributes it's killing to "the one who hit it last", and as bleeding/burning of enemy units happens on enemy turn, ALL enemies that bled out count towards totalReactionFire (except those wounded by grenade or a proximity grenade).
Noticed this when my AI units in Minigun tanks started getting Overwatcher commandment in XCF.
Easy (while not very elegant) fix would be storing wether the shot was reaction at the same place where "the one who hit it last" info is remembered.