Flame Totem with Three Dragons do not proc HoT on kill effect

The alternative is that they only use their own offensive stats.
Of which they have none.

They are a separate entity, but they draw offensive stats from your character. As such, they do trigger all your on-Kill bonuses - for themselves. If you have Life on Kill, then your Totem gains Life when it kills an enemy.
Herald of Thunder is a Buff active on the character. It is not active on the Totem. The Totem can trigger the on-Kill all it wants, but it still doesn't have Herald of Thunder active and thus it cannot actually do anything with the trigger.

It's a perfectly sensible argument when one considers the way Totems are coded.