Yes, that's correct. Though it's worth noting that most Hispanics in the Southwestern US are likely Mexicans:
Mexican-plurality areas are in pink on this map, FWIW.
I notice that there is a correlation between the Mexican-plurality and Spanish-plurality territories here and the parts of the Mexican Cession that Mexico proposed that it itself be allowed to keep in 1847 (specifically the territories below the blue line on the map below):
This makes me believe that the US grabbed too much Mexican territory in 1848. But of course too late to second-guess this right now, especially considering that AFAIK Mexican-Americans generally prefer to live in the much richer and much safer US than to live in Mexico.