##Part 1
There is a lot of historical context around answering this question. To start, here are some previous answers of mine that provide said context:
You also might find this answer from /u/Kelpie-Cat helpful as they go into some specifics on key concepts like terra nullius and the Doctrine of Discovery:
The first thing I need to elaborate on: Tribes, Tribal governments, and reservations were not "given" anything. We were not given rights, we were not given sovereignty, and we were not given any of the items you've listed as a characterization of being independent nations. Tribes are and always have been polities who exercise self-governance. We retain what has come to be called "inherent sovereignty."^1 This phrase means that our right to self-determination has existed since time immemorial and is passed along to future generations of our governments. Indigenous Peoples have always constituted our own "nations," so to speak. The issue at hand is that from a Eurocentric perspective, Indigenous Peoples don't typically qualify as nations, either philosophically or within legal theory. And because this is hardly taught in any meaningful way in countries like the United States, people are left with the Eurocentric rendition that is reductive and ignorant at best, racist and harmful at worst.
After the American Revolutionary War, the United States sought to solidify their newly acquired land holdings from the English. In continuing the colonial legacy of their former kingdom, the U.S. adopted what has become known as the Doctrine of Discovery. Essentially, this doctrine was employed by colonizing European powers to "legally" claim "discovered" lands that might be occupied by non-Christian inhabitants. In other words, in European (and later American) eyes, it robbed Indigenous Peoples of any recognized international title they might have to their own homelands, leaving them to be claimed and settled upon by Christian nations. Elements of this doctrine were cemented into U.S. legal tradition in the Supreme Court case of Johnson v. M'Intosh (1823), the same case that also clarified that the United States was the benefactor to previously occupied British territories and assumed radical title over these lands, as well as the right of preemption, or that the lands could only be sold to the United States. Though earlier cases, such as Fairfax's Devisee v. Hunter's Lessee (1813), had preserved the ownership of lands bought, sold, and retained by British citizens as stipulated by treaty, there were no exceptions for radical title made under treaties, in U.S. common law, or in federal legislation to protect land holdings of Native Americans outside of what is known as "right of occupancy," a right which may be extinguished by the federal government as outlined in Johnson v. M'Intosh.
Now... Despite all of that, Tribes were still recognized as sovereign entities, even in the early 19th Century.^2 Even though the United States didn't recognize any radical title over the lands occupied by Tribes, they very well couldn't walk into any lands and ignore the Indians there. This was a major concern for George Washington's administration in that they couldn't sustain all out war with the numerous Tribes both inside and bordering the U.S. frontier. Furthermore, they also adopted the British tradition of dealing with Tribes as sovereign nations. So there was precedent involved here too in terms of the policy approach of the federal government.
As we progress into the mid and late 19th Century, the United States developed the reservation system. There is an important distinction to be made here: there are reservations, then there is the reservation system. As the U.S. began expanding westward, they entered into legally binding treaties--hundreds of real, government-to-government treaties--with Tribes. Through these treaties, Tribes regularly negotiated for the protection and reservation of their traditional lands. While all of these treaties would come to be broken in one form or another and many other were not ratified on their original terms or were later abrogated and altered, many of the reservations today are a result of these negotiations and the active efforts of Tribes to secure their homelands. For the federal government who would quickly dominate through military supremacy, it was a matter of organizing these tracts of reserved lands. Because they had made many of the same obligations towards Tribes throughout many of these treaties (annuities, rations, education, protection), there was a need to systematize these reservations for overt logistical reasons and more subtle imperialistic means. So the federal government proceeded with the creation of reservations, but they would regularly try to negotiate for terms that were more favorable to them, obviously. This also included the creation of reservations that some Tribes would be forcibly removed to, reservations that were not the traditional lands of some Tribes, and reservations that were, in a sense, terminal.
But what these reservations served as (and continue to serve as) was a land base. Though we can debate the characteristics of what a sovereign nation looks like today, nearly all definitions agree that a sovereign entity must possess a land base that they govern. Here is our first identification of Tribes as sovereign nations. Though Tribes may not hold radical title to the lands we own, our occupancy title is what was preserved through these treaties. This means that Tribal governments actually govern reservations and are able to govern them how they see fit.
What complicates this matter, though, is colonialism and paternalism. While Tribes operate governments on their respective reservations, the federal government (and American society) never really anticipated that Tribes would last this long. There was a prominent zeitgeist throughout the 19th and up to the mid-20th Centuries that Tribes would simply cease to exist by becoming assimilated into the greater American fabric.^3 In an attempt to actualize this, federal Indian policy often had, what we call in public administration, moments of "punctuation." The policy would see some massive upheaval in how it was being enacted that fundamentally changed the policy approach. For example, the treaty-making process was ended in 1871 (but all ratified treaties before this point remained operable unless later abrogated). In 1887, the General Allotment Act was passed, which drastically altered the jurisdiction on Tribal lands. In 1924, American citizenship was forced on the remaining Indian population that did not receive American citizenship through other means. In 1934, the Indian Reorganization Act was passed, a piece of legislation that created a template for how Indian governments were to be structured. All of these moments severely altered the way in which Tribes could exercise their sovereignty (along with a bunch of Supreme Court cases that also regularly amended these confines placed onto American Indian sovereignty).
Edit: "Dominant" to "dominate."