Do you know that all of the burners and thermostats are working properly?

My guess for why this is happening is that the middle tank is cooler than either the terminal tank or the on-demand supply. As you use the water in the terminal tank, the water in the cooler intermediate tank refills it. The terminal tank probably doesn't have enough heating power to warm the water quickly, so it's unable to warm the cooler water on its way through. Then the on demand system replenishes both tanks and that water doesn't get time to cool in the intermediate tank, as it just passes through, so it remains hot.

Assuming a 2.5gpm shower head, three minutes would be 7.5 gallons, which would be in the neighborhood of 30 liters. So my guess could be wrong. A 30 liter tank would be about one cubic foot. (A 10L tank would be about .35 cubic feet, so a little over eight and a half inches on a side.)