Remember several things:
1) All objects are "existing" in CoE, which means coins, resources, objects, every thing exist physically.
2) The town by itself do not exist, it exist thru the charter that is signed between the Mayor and the count.
3) Taxes are paid to the Mayor (at least settlement taxes), not the settlement as the settlement do not really exist on its own
When you combine those 3 points, you end up with the fact that there will not be such a thing as a public treasury. The Mayor is responsible to pay taxes to the Count, not the settlement.
Then remember that taxes are fixed by law and contract and they state what you have to pay, not a percentage of something, they will say x amount of grain, Y amount of iron and z coins ... without ever knowing what the settlement population paid as taxes. Maybe your settlement people paid some chicken, a few pigs, logs and some coins, but no grain and no iron, but your count expect iron and grain, so you the mayor need to provide those as your tax to the count, what you do with what the people of your settlement gave you is your business.
But, as much as tax go to your pocket, spending for the town comes from your pocket too. The south tower need repair ? that's on you, how you do it is up to you, maybe you trade work on the tower for tax to people or you ask for materials used in the repair as tax and pay for the work or just pay yourself and ask other things as tax, or do not repair the south tower, after all what is that tower for ? the settlement never been attacked and the upkeep is only a dead wait, or even you decide to tear the tower down, use the materials to build new houses or something.... all is up to you.
the domain is yours to rule for better or worse, you can chose to exonerate your people from taxes, it will not change the fact that the count will expect you to pay full tax to him.