It depends on where you live. In my country parents love to meddle their children's lives. So you need to know what kind of parents he/she has.It is also necessary to introduce each others family .
You must be asian
I think they've met each other's parents before (since they're already familiar with each other's siblings), so what they meant must be greeting both family after marriage which is some kind of tradition (I think?). I know some countries have that tradition, but I don't know about Japan haha
They'd been dating for 4 years and they lived together... But they didn't meet each other's parents until after he proposed to her???? That's just weird to me.