Only one member from your team is responsible for registration and payment. Once complete, there is no other action needed from the other team members.
When on the registration page for an event, tap "Add Team Members" and search for the name of the parent account. For privacy reasons, dependent accounts are tied to their parent accounts.
Accepting an invitation for a dependent: The parent account will recieve the team invitation on behalf of their dependent, where they will then select which profile is accepting and away you go!