Credit card details are tied to the admin who placed the last transaction so if you're another admin on the team and you're ready to make a purchase, you'll be required to enter new billing information. If no new credit card details are entered and your Business subscription is set up to auto-renew, then the auto-renewal will charge the credit card associated with the last online transaction.
This article refers to a feature unique to Dropbox for Business. Dropbox for Business is designed for projects, groups, and other organizations that want to share the same Dropbox storage quota with all of its members. If you're interested in learning more or want to sign up, visit the Dropbox for Business webpage.