Then it is pretty simple. The man in charge invoices each pilot for the hourly rate plus the fuel cost. If a particular pilot flies for an hour at 40 litres/hr then he will obviously get a smaller invoice than another pilot who flew for an hour at 60 litres/hr.
I imagine that invoicing in arrears also has a significant admin cost, and probably eventually a financial loss, where getting money out of people a few days/weeks after they have flown is much harder than getting it on the day that they've flown.
If they can't work out their own bill on the day and arrange for payment then, then I reckon it's only a matter of time before you get stung, and even if you don't you'll send a lot of time making reminder phone calls.
dp