Sorry to hear this happened. I'm picturing you had the gray drain valve open and went to sleep feeling that everything was taken care of. Definitely get it cleaned up as quickly as possible to prevent as much damage as you can.
It's too bad the manufacturers don't advise you that they have plumbed the bathroom sink this way. but I guess that warning is only good for the original purchaser anyway. I'll bet that the kitchen sink drains properly into the gray tank, but I would verify that before trusting it.