You know, I originally thought the explanation would be something logical (well, logical for a fantasy setting), like "you fertilized the eggs when your blood got on them, thus exposing them to your genetic material/life force/whatever", in part because they called attention to the fact that his hands got bloodied and he got his blood on the eggs in the first chapter.
Now I know the actual explanation, and I sort of wish I didn't.
Honestly, I'm half expecting it to turn out that the rat is an arse and lied to both of them, or at least that it was the blood but her thinking of him made it so that only his blood could hatch them.
Also, in the bottom left corners of pages 13 and 14, Kunpei speaks for all of us.
EDIT: Wait, is she planning on sleeping in the same bed as her babies?! That's a terrible idea!