NEW DELHI—Smartphone maker Vivo became the latest Chinese tech firm to face tax scrutiny in India, prompting China’s embassy to warn that “frequent investigations” are damaging the confidence of Chinese businesses operating in the South Asian nation. India’s Enforcement Directorate, a law enforcement agency that investigates financial crimes, alleged Thursday that Vivo Mobiles India Private Ltd. and its associated companies sent earnings abroad to show losses in India and avoid paying taxes.