It seems the integration process worked differently on a Clan-by-Clan basis.
The Ghost Bears appear to have been the most organized, working with established local leaders and promoting them to positions of authority to ease the transition. Their outreach to the conquered civilians seems to have facilitated buy-in to the Caste system from the Rasalhagians, especially once former leaders like Ragnar Magnusson were inducted into the ruling Warrior Caste.
The Smoke Jaguars seem to have simply imprisoned any captured enemy soldiers and relied on propaganda broadcasts to inform the civilians of their new lifestyle. (Since they exclusively hit Combine worlds, they didn't have to introduce the concept of Castes, so that wouldn't have been much of a sticking point.) They massacred any civilians that resisted their new caste assignments or fought against Warriors (most notably on Turtle Bay).
While published materials suggest the Jags looked down on freeborns and refused to take any captured Spheroid warriors as bondsman fighters, MechCommander prominently features militia auxiliaries on Port Arthur composed exclusively of former DCMS troops now serving as Jaguar second line garrison staff. The fact that Judith (a ROM mole) was taken as a Bondsman to be a technician indicates that the Jaguars do, indeed, take freeborn bondsmen.
The Wolves seem to have set up processing centers where individual skills can be assessed and caste assignments made accordingly. ID cards are issued and required to be displayed upon the request of a Wolf Warrior or other official, and are presumably required to purchase food, travel, or do any number of functions. The goal is to give civilians incentives to join the Caste system by penalizing them for not getting with the program. The Warriors can then hunt down the resisters who go Bandit and head for the hills.
The Jade Falcons also appear to have processing centers. In the Cartoon, the crew of the Kwaidan are detained, told they will be inducted into the Merchant Caste, and put in a paddy wagon bound for a re-education camp. They escape and reclaim their DropShip, but had they made the trip, they probably would have spent a few weeks being indoctrinated before being sent back out into the world under the supervision of Clan born Merchant Caste members. The Somerset Military Academy had been converted into such a re-education camp, with cells, musters, beatings, and large screens constantly blasting propaganda and information about the Clan Caste system. (Granted - those scenes are from a Solaris Broadcasting Company entertainment program, so their accuracy is questionable, but it's what we have to go on.)
Based on the Karston scenes, it could be that only those who actively resisted the Clan conquest were subjected to such camps, while the rest were simply registered, assigned a Caste, and assigned tasks without significant supervision until/unless they got out of line.
The Steel Vipers apparently handled the control of the civilians very poorly, expecting them to act like Clan natives, and enacting brutal crackdowns when they failed to do so. This resulted in significant unrest in the territories they assumed from the Jade Falcons, and made it all the easier for the Falcons to take them back, later.
We don't really have much data on how the Nova Cats treated the conquered civilians, since most of the focus on them came after they switched sides and joined the Star League.
The Diamond Sharks, of course, never had any conquered civilians to administer.
