In the later seasons we get an impression of the Dominion as somewhat Nazi-like in that they control every aspect of your life. But when we actually see cultures in the GQ we get two basic types of worlds: Worlds that the Dominion ignores but know that if they anger the Dominion they'll get destroyed, and worlds that have been driven into the ground by the Dominion.
Also it's been noted that Ferengi ships are never attacked by the Dominion.
This leaves me to believe that so long as a planet does what it's told, the Dominion are very 'hands-off' dictators. They pretty much see whatever the planet chooses to do as being of no consequence, unless they get too powerful or become a threat.