-(으)니까 supplies the trigger and 생각나다 is the memory arriving on its own: 가족 하니까 생각난 게 있는데 'speaking of family, that reminds me of something', 청소하니까 생각난 건데 'talking about cleaning brought this to mind'. [Noun] 하니까 means 'now that you mention [noun]'. This is the ordinary way to steer the conversation to whatever it just jogged loose.