They do have some factories, but there are people there who will start fighting them as soon as they start breaking property. The enchantment only lasts as long as the Achamites aren't being aggressed, which includes their property, and so they will have some fights on their hands.

If they are both prepared to fight a bunch of soldiers, we can do some rolls to see what sort of destruction they can accomplish while in the city.

Also yes, the tithes are put into general circulation so there are a lot of warehouses holding that sort of thing. About half of Achamoth's economy is in tithes, and most of that goes directly into the pockets of Achamite citizens. Some of it does go to the Citadel, mostly just what it needs to function, but it isn't greedily hoarded anywhere. The wealth taken from other cities is spread around, though sometimes the most influential members of the city take undue control over the specifics.