How Does the University of California Major and Alternative Major Preference Work In Practice? Strategies?

For UCSB CCS specifically, we are a little unclear on how this works.

If a student lists a CCS major as one of their two choices, and is subsequently admitted to CCS, are they only offered admission to one of the two majors, or are they offered a choice to enroll in either the CCS major or the other major? It’s particularly confusing if the other major of interest is in engineering.

The CCS web site says,

When selecting two majors on your UC Application, you should list your preferred CCS major as one of your choices (preferably the primary), unless you are also applying to the College of Engineering (CoE). CoE requires Engineering as your first-choice major, so CCS can be your second.