To give some additional context here: there is no Indian Removal Act, but this does not stop the process of Indian Removal. Even opponents of the act like John Quincy Adams and Henry Clay had previously agreed with the principle of relocating Native Americans, but they opposed the act because they believed it gave too much power to the president and tribes should move voluntarily instead. (This ignores the fact the tribes very much did not want to move). So in this world, the president was not authorized to "swap" land with Native Americans, forcing creative schemes like this into existence. Indian Territory would be used as an area to relocate the Plains Indians from Nebraska and Minnesota. Many members of the Southern tribes and Comanche would also settle in Indian Territory, although the federal government would not recognize the latter as sovereign nations there.
The Creek face a similar fate to the Cherokee and end up moving to Texas as well in the late 1830s. The Seminole, Choctaw, and Chickasaw remain in Florida and Mississippi, although they are coerced into selling more land to the federal government. Other tribes which were affected by the Indian Removal Act, such as the Seneca, Cayuga, Wabash, and Pottawatomie, retained more land in New York and Indiana.
Mexico's actions do not indicate a policy of generosity and friendship with indigenous peoples, either. The Cherokee and Creek were welcomed in as bulwarks against American settlers in Texas, who were widely distrusted by the 1830s. They would also, along with the native Waco and Tawakoni, be useful allies against the dreaded Comanche, who the Mexican government would continue fighting until the 1860s when they were forced to settle on a small reserve in Nuevo Mexico.