How much damage are you dealing with it? Alpha Strike is somewhat confusing because whether it gets the bonus damage or not, it appears to be just one hit (though it is treated as two, in that they CAN hit or miss separately, and they can crit or not separately -- at it also is penalized twice for shields and sandstorm).
Typically on an aquatic my moths will show ~550-575 damage for an alpha strike for which neither part crits. (Since I almost always fight aquatics with them, I can't recall the damage they do against non-aquatics
Double-checked the wording on the ability. It is "additional damage" and not "hits an additional time" if you go first (what Thrash says). So its not as confusing as I thought, cause by the tooltip it *should* be just one number you are seeing.