How do primary and secondary majors work in a UT Austin application?

So I am applying to UT this summer and am wondering how the application process works.
My major choices:
1st: Finance(Mccombs)
2nd: Economics(COLA)

I heard from some people that if you don’t get accepted into your first choice major, they don’t even look at your second choice and just give you a list of majors that are available for you to go into. Is this true or do they do the holistic review for the second choice as well?

If you aren’t accepted to our first, you’re considered for the second.

In engineering, business, and computer science, you aren’t considered if you don’t put them as your first pick.

For example: 1st pick business, 2nd pick engineering. Engineering will not look at your application.

It’s most common to hear of someone getting to pick out of a few majors if you’re in the top 7 percent and aren’t accepted to your majors.