Are there any CFOs among us? Need advice

We're now introducing a new feature in Approveit (https://approveit.today/) - cost centers. it allows you to allocate budgets for each department or project, and follow the amount you're spending on it. The question: Should we subtract the paid amount from the budget that covers the factual payment date, or should we subtract the paid amount from the budget it was supposed to be paid from (according to the invoice due date or contract terms, whatever), but was factually paid at an earlier/later date making it come from a different "cash pile"?