During the Đại Việt period, the Vietnamese states of that time trounced Song Dynasty China, crushing armies in the hundreds of thousands in border actions, and held back multiple invasions by the Mongols under Kublai Khan during the Yuan Dynasty, including totally destroying the Mongol navy at the Battle of Bạch Đằng. The Mongols/Chinese, in fact, showed very little ability to win any victories at all against the Vietnamese in this period, and in fact, suffered what seems to have been consistent defeats, one after another.
Why then did the Trần Dynasty (Northern Vietnam, today) and the Champa (Southern Vietnam, today) both agree to become tribute payers to the Khans, a relationship which lasted until the end of the Yuan Dynasty?
Extra Credit: what exactly did the tribute consist of, and how were the payments made?
If it’s okay with the mods, I would like to make a correction to some of the information you presented in your question description. This won’t be an answer to your question though, which is a bit out of my wheelhouse in terms of specific policy (though I can say that in general, tribute relationships existed with China so that China would provide support and recognition for whichever dynasty was in power; if a rebellion happened, China would in theory help quash it, and this did happen in practice too). I can come back to that for you later though I think.
However, I do think it is important to point out that Champa, which is in what is modern central Viet Nam was not Vietnamese and was not a part of “Viet Nam” in terms of society or culture. Champa was ruled by Cham people, who are still an ethnic minority in Viet Nam today. The Cham are an Austronesian-speaking group and are culturally and linguistically much more similar to the people of Maritime Southeast Asia, such as the Philippines and Indonesia. Champa and Viet Nam actually had a very long rivalry with each other, much more heated than between Viet Nam and China in fact. Champa nearly defeated Viet Nam entirely in later centuries, however, VN recovered and ended up being the ones to conquer Champa for good. What is also interesting is what the Cham ended up contributing to modern Vietnamese culture and society. In central Viet Nam after Champa’s defeat, for example, marital practices differed significantly from those in the north due to influence from Cham culture. Even the famous Tay Son Brothers, the leaders of the Tay Son Rebellion and who are national heroes in Viet Nam, were actually likely at least part Cham in background rather than being Vietnamese.
Anyways, I thought this was important information and in fact, up through the Nguyen Dynasty, Viet Nam was actually a major colonizing force in Southeast Asia, essentially eliminating both Champa and Angkor and threatening Chinese dynasties as well. It was not simply a difference in names of polities.