We know that Teddy and his parents lived in the Segowlee cantonment in India, so Rikki-Tikki-Tavi must have originally lived close by before the mongoose joined the human family. Before he came to live in the English family's bungalow, Rikki lived with his own parents, but
One day, a high summer flood washed him out of the burrow where he lived... and carried him, kicking and clucking, down a roadside ditch.
It was young Teddy who found Rikki, and he thought the mongoose was dead. But Teddy's mother convinced her son to bring him back home, and after being dried out, Rikki "opened his eyes and sneezed." Rikki apparently never tried to return to his own burrow and find his parents since he loved Teddy and quickly became an important part of their family.