Historical side note: tantric practices developed in India as one of the very late stages of its development before it faded away in that country. It was at this time that Buddhism spread from northern India, hotbed of tantra, to Tibet.

So it's a bit more accurate to say that tantric Buddhism went to Tibet (and merged with Bon's animism), and then hung on there while it died off in its country of origin.

(Tantric Buddhism also made its way from India, through China, and to Japan, where it survives as Shingon Buddhism)