Ouch. Well, then I hope it's not early; is it a high school or lower test? XD Then I can help you.
Anyway, I tested things out some, and with both the Amurites and Scions to see if it was just the Amurites for some odd reason.
Any temporary summoned unit, it seems (tested with fireballs, fire elementals, wraiths, specters, and skeletons) will increase unit supply costs when they attack and die. Fireballs will increase it if they attack and win, because they die instantly. The other temporary summons do not increase it any when they attack and win, because they didn't die from it.
Skeletons, however, being permanent summoned units did not increase the unit supply costs upon death.
I also tested it with FFH2 041D, and it did not increase it any, so it must be a problem with Fall Further.