Flushing the toilet when there's nothing in it but differently coloured water is a waste, but I understand why you have to do it in a social context. I would prefer not to needlessly strain my shitty pipes, but I prioritise other people not needing to know that I piss just like they do.
Anyways, this is a very obtuse way of asking how many times does a person have to come to your apartment before you can shamelessly not flush the toilet after (visibly) peeing?
If your water comes from the same watershed that your sewage returns to, there is no reason to do this. The only thing you are wasting is an amount of energy so small that it is less than leaving one charger plugged in for an hour when you're not using it. Water treatment and processing for a couple of liters of water is miniscule in terms of energy use.
It only really makes sense to "let it mellow" if you're in an environment with water shortages or hooked up to a septic system which is where the concept originates.