Many came from Wuhan, leaving just ahead of a Jan. 22 ban on travel from the area where the coronavirus began to spread.
Some say the move will further undermine Tibetan national identity, already weakened by Han Chinese migration into the region.
Similar Ministry of Education directives were issued in 2018 and last year.
Sources in Tibet say many more monks were arrested in the area since.
Followers believe an announcement citing 'illegal activities' was scripted by Chinese authorities wanting to reduce the centers' influence.
Concerns over this year's observance may reflect worries about ties to a ceremony in India led by the Dalai Lama.
The Tibet Policy and Support Act of 2019 passes the House Foreign Affairs Committee with bipartisan support and will next go to the full House for a vote.
The detentions follow Chinese government warnings against posting illegal content on the WeChat messaging service.
They must demonstrate political reliability and support of China's rule in their homeland, instructors say.
Anya Sengdra is sentenced to seven years for 'disturbing public order' after complaining online about official corruption and environmental abuses.
Yonten's protest brings to 156 the number of Tibetans who have set themselves on fire to protest Chinese rule in their homeland.
Representatives from communities in India, Nepal, and Ladakh say the selection process must remain in the Tibetan people's hands.
Exile sources say 24-year-old Yonten “died on the spot” and is the 156th such Tibetan protest since 2009.
Gathering in Dharamsala declares traditional Tibetan method of choosing successor “will be followed.”
Anya Sengdra had set up WeChat groups to discuss corruption, good governance, and environmental protection, likely angering authorities.
Heightened security measures follow two leafleting protests this month in Kardze's Sershul county calling for freedom from Chinese rule.
The protest follows the detention of four monks who scattered leaflets calling for Tibet's independence in a protest earlier in November.
US Ambassador-at-Large for International Religious Freedom Sam Brownback says that more pressure should be applied to Beijing over China's abuses of religious freedom in Tibet.