This question depends mostly on who you ask.

The Chinese answer, which is based on the assumption that "China" is made up of five races (Han Chinese, Mongol, Tibetan, Manchu, and Turk) they would say alternatively, "Always" and "during the Mongol Empire which took control of Tibet in the 1240s." Prince Godan (often referred to as Godan Khaan) took it upon himself to conquer Tibet after his ancestor Chingghis Khan had been killed in fighting the rebellious Tangut. The Tangut were fond of Tibetan lamas and spiritual teachers and suggested to Godan that he contact the head of the Sakya Monastery for his own spiritual purposes. Godan sent a message to Sakya Pandita "instructing" him to report to Godan's camp and then to tell the other Tibetan chieftains and monasteries to submit to him. Sakya Pandita traveled to Godan's camp, saw the power and might of the Mongols, and conceded, writing letters to the remaining Tibetan principalities insisting that they submit to the Mongols rather than be destroyed. The whole of China wouldn't submit so easily, and would linger on into the 1270s resisting Khubilai Khaan's armies for decades to come.

The Tibetan answer is often more nuanced but can be alternately taken as 1720, 1792, 1950, or 1959.

Throughout the 1600s, the Fifth Dalai Lama was busy establishing his legitimacy across Asia. He became involved in the middle of the conflict between Mongol tribes and the (now) Manchu-dominated Qing Dynasty of China. The inability to locate a Dalai Lama, and infighting among Mongol tribes, and the death of Tibet's king Pholhanas (Po-lha-neh) created the power vacuum anew. The Qing were concerned that the fighting would spill over into China so took up the cause of the Seventh Dalai Lama, Kelzang Gyatso, put him at the front of an army, and quieted the fighting installing him on the throne in Lhasa. The Seventh Dalai Lama wasn't much interested in governing, but his influence (and undoubtedly the acnowledgement that the Qing were no longer silent observers) had a calming effect on Tibetan influence. While there was no permanent Qing or Chinese presence yet, it's undoubtedly true that decisions in Beijing had direct effects in Tibet at this time.

The Manchu made a concerted effort to patronize Tibetan monasteries under the idea that more monks was less potential soldiers. This effect was felt almost immediately when the Nepalis invaded in the 1790s and Tibet was unable to fight them off, with the fighting looming uncomfortably close to Lhasa. The Qing sent reinforcements and pushed back the Nepali army, and managed to wrest a treaty from Kathmandu in Tibet's favor. But this time, a Manchu army, and two Manchu officials called "Ambans" were stationed permanently in Tibet.

Well, not permanently. The Xinhai Revolution took place in 1912, kicking out the Qing from China, and the Ambans from Tibet. The fighting was fierce in Lhasa, and led directly to the Tibetan Declaration of Independence written and signed by the Thirteenth Dalai Lama, declaring complete independence from China.

Alternatively called Tibet's "Peaceful Liberation" by the Chinese, and "the Chinese Invasion" by Tibetans, the Battle of Chamdo in 1950 ended Tibet's experiment with independence. The People's Liberation invaded Tibet, took up residence in Lhasa, and forced the government's ministers to sign the Seventeen Point Agreement, which seemed like a pretty good deal on paper, but the deal (which in a nutshell, said that Tibet would be free of Communist reorganization without Tibetan approval, and that Tibet was still free to make her own decisions) broke down within nine years as conflicts within the Chinese army, and between Chinese and Tibetan officials over exactly what constituted "Tibet," broke down the fragile peace that was maintained between the Central Tibetan organization and the People's Republic, resulting in the Dalai Lama's flight from Tibet in 1959 and his residence as a refugee in India. The hardest-core Tibetan nationalists will insist that Tibet was 100% independent with little more than advice, lip service, and religious patronage coming from China until 1959. They will insist even that this was the relationship that the Dalai Lama and Mao were discussing before his flight in 1959.

Regarding your question, however, there's a lot of room for nuance in the question, requiring us to define words like "Tibet," "China," and "control."