Any spell you cast that doesn't have the type creature will cause Soulblade Djinn's ability to trigger. If a spell has multiple types, and one of those types is creature (such as an artifact creature), casting it won't cause the ability to trigger. Playing a land also won't cause it to trigger.
Soulblade Djinn's ability goes on the stack on top of the spell that caused it to trigger. It will resolve before that spell.