I had a chat with support and here is how the whole thing works:
1. No invoices for paying money to top-up the account.
In other words, if you happen to add $1k now and spend that money to buy 100 domains next year (ie. 100 small invoices), prepare a hefty work bonus to your accountant if he manages to handle the mess for providing invoices of next year for something that shows in the bank this year.
2. As mentioned, receipts can be issued for each purchase using the account funds *but* it doesn't work automatically; we need to add the details manually at the time of the transaction by clicking the appropriate button. If, for any reason, we omit that step then the invoice *will not* contain our details (ie. it will be an unusable, devoid of details, receipt) and the only solution is to contact support for them to add the necessary details manually.
3. When I asked them what happens with transactions that the user is not present to click the 'add details' button (eg. in the case of auto-renewals) their response was that, in that case, the order is generated without an invoice address which means we need -again- to contact them to set up the invoice properly.
This is way too messy for my liking. I planned to add Spaceship to the small list of registrars I use regularly but, until they fix this mess, that is not going to happen.