It's not necessarily true that each baby will have its own placenta.. I've read that triplets can have 1, 2, or 3 placentas, where one may have its own and two others share one, or each has its own, or they all three share, etc.. If I'm not mistaken, though, I think it's more common that multiples share a large placenta rather than each having its own. That's been my experience, too..
As in, baby...baby...baby...one afterbirth...then she's done.
Funny thing is, I've never really thought much about it until now. I do remember sorta curiously looking at the placenta after one of ours had triplets, though, and noting to my wife that you could see where each of the three tiny cords were attached.
If she passed placenta and seems to be done pushing, and if the baby's up and nursing...I'd say all's well.
Congrats.
(I assume she healed up OK from her previous injury?)