Thanks for all the replies. Maybe I did let the water boil a little bit too high, instead of simmering. And because of that, maybe drops of water did get into the custard. Well, I still have extra of all the ingredients, and since Marielle has made this same recipe and it was okay, I'll try it again and see what happens.
Although the one thing that is really stumping me - why the plastic wrap touching the top of the dishes? Is that to prevent a hard crust being formed?