According to the User Guide, invoices issued to the buyer will appear in the buyers Mailbox. I made several Direct Purchases recently but received no invoices by mail, until I noticed them listed under Invoices to be paid. Perhaps this is bug to be sorted out.
Invoices are now auto issues when the manufacturer accepts the order from you. As soon as you see a notice that the offer has been accepted, the invoice will be in your “Invoices to be Paid”.
We will make sure to update the guide.