How is the plot advanced when Nagaina started targeting the human family?

The part when Nag and Nagaina decide to target the human family in the house furthers the plot as part of the rising action. A few hours before, Rikki-tikki proves his quickness against the cobras when he dodges their come-from-behind sneak attack. Rikki-tikki then proves his lethality when he kills Karait. At that point in the story, the cobras know that Rikki-tikki is dangerous, and he knows that they are dangerous. An uneasy truce could have been established; however, Nag and Nagaina decide to escalate the tension. The snakes believe that if the humans are eliminated, Rikki-tikki will leave of his own accord or will be easier to hunt.  

"I will go, but there is no need that we should hunt for Rikki-tikki afterward. I will kill the big man and his wife, and the child if I can, and come away quietly. Then the bungalow will be empty, and Rikki-tikki will go."

Rikki-tikki overhears the conversation between Nag and Nagaina. Rikki-tikki feels it is his duty to protect the family, so he knows that he must kill Nag to eliminate the threat. That causes a further escalation in tensions because Nagaina wants vengeance. The plot continues to rise until the climax of the story when Rikki-tikki follows Nagaina down into her snake hole.