Yes, he will need to apply. That is just his intended major. Terry requires a separate admission. I’ve got a finance major and if that is what he settles on they will look at his GPA and core Terry classes (not his total GPA), his ACT/SAT score and his score on the accounting admission test. Highly recommend taking that immediately after you finish accounting 1 even if that means you stay a few days later.
Also, highly recommend paying for Skoolers for accounting. Accounting is a weed out class and often test scores are in the D range. There are videos and packets that reinforce the classroom stuff, and kids that do this tend to do a lot better. There are some kids who just “get” accounting but that is not the majority! There are also a lot of accounting labs and resources to take advantage of. My advice would be to investigate those and let your kid know about them at the beginning of the semester. My kid was scrambling!