Cities always gain money from things like taxes and trade. The only reason that they might seem to be losing money, is that they will have to pay their part of your army upkeep, wich might be bigger than the income from the city. How much they pay is decided by how big percentage of your total population lives in the city, if 20% of your citizens live in a city, it pays 20% of the upkeep.
Because of that, your big cities will be paying a large part of the upkeep, and might therefore seem to lose money, while your small ones that pay only a small part will show a positive income. Extermination of a city will NOT increase it's income, even though it might seem like that. This is proven by this example:
You own Syracuse, Lilybaeum and Messana. The upkeep for your army is 20.000. Syracuse has 10.000 citizens, Lilybaeum has 6.000 and Messana has 4.000.
Syracuse show a income of -1000 (beacuase of paying 10.000 denarii of the upkeep, while earning 9.000), Lilybaeum +500 (after paying 6.000 denarii for the upkeep and earning 6.500) and Messana +1000 (after paying 4.000 denarii and earning 5.000).
Your total income for the whole empire: +500/turn.
Now let's say you exterminate Syracuse because of it showing an negative income (killing 7.500):
Syracuse shows an income of +500 (after paying 4.000 denarii and earning 4.500), Lilybaeum -3.600 (after paying 9.600 denarii and earning 6.000) and Messana -1.400 (after paying 6.400 denarii and earning 5.000).
Your total income for the whole empire: -4.500/turn.
As you see, exterminating will only spread out the upkeep to other cities, while decreasing the income from the city, even though it might show a higher income. You will get around 20.000 denarii when exterminating, but in four turns the decreased income will have eaten up that, and after that you will have less money.

Experienced RTW gamers would be more than welcome to complement this if they think I have missed/not been clear enough about anything, and I will add/change it here.