No I'm afraid I'm not really following. Can you explain your payout method more clearly, from start to finish?
They keep the transaction fees for themselves. They don't distribute it to the miners. They use these fees to cover the fees involved in sending payments out to users. Since their payments are 'instant' they also need funds available to send payments out that are requested while blocks are still 'immature'. The fees are also used for that. That's how I understood what was said.