This isn't 100% on-topic, but my last visit with my shiny new OB (sniff-miss my midwife who won't do twin homebirths) had this conversation.
He was weaving his web of all the wonderful reasons why I should seriously consider an epidural. He's delivered a good number of twins and told me sometimes the body 'thinks it's no longer pregnant' after the first baby's birth and the placenta starts to come out. It's a dire situation then and an emergency C-section has to happen. (I have one placenta, two sacs)
I know, he sounds like he may be awful. I just met him, so I'm still figuring that out. In the good news dept., he is rarely does episiotomy, strongly supports vaginal birth, and is comfortable with the second twin being breech. He told me he'll just thrust his arm up me and grab it's feet and pull. That's when he once again mentioned the epidural.
Don't worry. If I get to term (37 weeks), this birth is mine and he'll just be a bystander. My HB midwife iwill be my doula too so that helps.
Well, anyway, it's nice to see how seldom that placenta before #2 scenario must happen.