Padmasambhava was invited by Trisong Detsen the king of Tibet not Western Tibet. He ruled the area which is about 2.5 million square KM, twice the size of the so-called Tibet today by Chinese (Tibet Autonomous Region) whole of Tibet which include the Tibet. China has merged the half of Tibet into Sichuan, Yunan, Gansu and renamed Amdo as Qinghai. The present Dalai Lama's family members and many in the Qinghai province are descendent of the Tibetan soldier sent by Trisong Detsen to guard the border in 8th century. The king of Western Tibet you are referring to happened much later about 200 years after Padmasambhava's visit. Yeshi Vod invited Atisha Dipankara from Vikramshila university in 10AD to revive and revitalize Buddhism.