Yes. His parents immigrated to the USA in the year of his birth. They would have needed 5 years residence to become citizens.
RE: his parents immigrated to the USA in the year of his birth
Vivek was born in 1985.
His Wikipedia page only said this : his father worked as an engineer and patent attorney for General Electric, while his mother, Geetha Ramaswamy, a graduate of the Mysore Medical College & Research Institute, worked as a geriatric psychiatrist. No mention of WHEN they immigrated to the USA or WHEN they applied for US Citizenship.
Do you have a good source to back up your claim?