It is likely that Romans made no distinction between today's terms integration and assimilation. They did everything that was necessary for the expansion of the Roman empire and worked from experience. Due to the communication lag between Rome and conquerors in distant, marginal territories, there had to exist directives/guidelines on how to deal with newly conquered cultures/tribes.
While the Romans adopted a lot of foreign culture as well (e.g. Greek philosophy, mythology), they likely didn't allow conquered tribes to practice their religion/language any more (?). That's probably the rough border line between integration/assimilation compared to today's meanings. Maybe they even married foreign women and killed foreign male adults/children to "speed up" cultural assimilation.
What known and/or documented procedures did conquerors/military tribunes conduct to assimilate foreign cultures in the best way? What was "officially" prescribed by the Roman senate and philosophy?