Yet, of course, Ulysses still calls Legion his brothers, and still favors them in comparison to the NCR.
Moreover, Ulysses is furious with the White Legs for attempting to honor him and not the Legion.
Note how Ulysses hates the idea that he would be honored, and not the Legion as a nation.
When asked why Ulysses didn’t just kill the Courier in Primm, Ulysses replies:
Since the encounter Ulysses had at Primm was likely just months or maybe one or two years before Lonesome Road, this indicates that Ulysses was recently respectful of Caesar’s orders, and Caesar’s rule.
But this doesn’t mean, necessarily, that Ulysses loves Caesar. (Ulysses actually never uses the word love.) What this means is that Ulysses loves the concept of a powerful nation that operates with the Legion’s same sort of strength and authority.
Ulysses calls Legion his brothers. Perhaps, to Ulysses, the question of Caesar’s authority is just a sidenote to the loyalty shared amongst people.
Ulysses is the sort of person who would prioritize a nation before a people. He’s done this before. Participated in spying and violent acts for a strong nation because he believes that a strong nation is virtuous.
That’s why The Divide being destroyed angered him so. It was the destruction of a nation that he had some faith in.
So the conclusion I believe can be drawn is that Ulysses is aware that Caesar is basing a nation off of the historical Roman Empire, yet this doesn’t matter to him. He’s aware that Caesar may fall and that the Legion is misguided, but still aligns himself more closely with them. (He respects a Legion courier more easily.)
It’s not that Ulysses is Legion-aligned or not. Even if he is not specifically working under Caesar’s orders, his personal political philosophy is in alignment with the Legion, and with a strong nation. He is willing to commit great crimes against humanity (such as nuking the NCR’s main supply line to starve them to death) if it means that a strong nation will be formed.