Tumby is often used as a nickname for people coming from South India and Sri Lanka. The plural form would be Tumbies. It is derived from the word Tamil as both South India and Sri Lanka have large Tamil populations. South Indians and Sri Lankans tend to be shorter and darker than other South Asians and belong to the Dravidian race of original Indians. The term is not offensive.
Hey who is that Asian boy over there? Is he Sikh or Afghan? No he looks like a Tumby.