Consolidated billing is now a feature of AWS Organizations. The information provided in the Billing and Cost Management documentation might be out of date. For current information about consolidated billing, see Consolidated Billing and AWS Organizations in the AWS Organizations User Guide.
When the linked account owner accepts your request to pay the charges for the account, you immediately become responsible for the linked account's charges. If that happens somewhere in the middle of the month, you're billed only for the latter part of the month. The linked account owner is still billed for the first part of the month, as shown in the following diagram.