Well, since golems are made and maintained by magic, it seems odd for fire to be used by wood golems. Seems out of theme to me. Idk.
It doesn't seem consistent with bein a golem. Cuz a golem is a created construct. And yet, it's creating a fireball? WTH?!!!
But it makes sense for mages to have fireballs. Y? Cuz they have the training required to cast fireballs. Furthermore, in most stories/games involving magic, when a mage makes a fireball, s/he summons it above their hand. And most mages are as affected by things such as heat as badly as normal humans. In fact, it usually takes a lot to bring down a mage. (Unless you manage to stick a dagger or sword in them.) At least, that seems to be my experience by reading fantasy books and playing fantasy games.