Spoils of War from 
Face of the Mountain procs from absolutely everything cast from a melee champion.
Example. Nasus E. Clearly not a melee attack, and yet executes minions as if it was. That is just one example of MANY instances I have come across me executing minions when i should not, according to the item. Either it is broken, or PLEASE update the text.
V~
The boards have scared me. When I saw the title I thought it was about to be another one of those false bug reports with thresh and Relic shield.
As for your main post I have seen this when I play Alistar and I use my Q and instantly use all my charges even though the minions were not low enough for his Q to kill them.
Fyi, the Face of the Mountain proc for execute is by champion type, not abilities/skills. So if you are classified as a melee champ (like Alistar, Nasus, Braum, etc) you can use ranged "spells' that will execute the minion.
Did it execute them, or were they just last hit and you got the shared gold?
Remember, FotM has an execute portion AND the shared gold passive, they aren't mutually exclusive. Ranged champions can use spoils of war if they last hit properly, and spells can still kill the minions for gold (but won't execute them like an autoattack would).
