If you don't control both an artifact and an enchantment at the moment Kami of Terrible Secrets enters the battlefield, its ability won't trigger at all. If the ability triggers, it will check again as it tries to resolve. If you don't control both at that time, the ability won't do anything.

The artifact and the enchantment may be the same permanent.

Its terrible secret is that it always forgets to call home on Mother's Day.