Auburn has 4 rounds - the first deadline is Sept 15. They are not a rolling admission school like Bama is.
Housing does not open until Nov. you get your time slot end October if you apply by Sept 15th.
So you needn’t rush. You will have ample opportunity.
Auburn is a Common App school. They have their own app too if you’d rather use that. Common App has an essay but each school sets its own parameters. So if Auburn doesn’t require one, then you won’t need one if you choose to use Common App. The reason to use Common vs the Auburn app is if you plan other apps that use Common. It saves you from repetitive work.
If your student is at their strongest - meaning you don’t want to wait for first semester grades or another test score, apply by Sept 15 and you’ll be fine - yes for housing.
They are using FUUD tactics to unnecessarily panic you. To many, that’s good, classic marketing.