There is an upper and lower half in every region. They use to never put 2 teams from the same conference in the same half of the region. At times in the past if a conference has 9+ teams they could not avoid this.
Now present day, Even if a conference has 8 or less teams, there is a chance two teams from the same conference could be in the same half of a region. Most times when this happens, it usually are 2 teams that are unlikely to meet up according to their seed. For example a 6 seed and a 10 seed. Both are in the lower half of a region, but those seeds would only meet in the Sweet 16. Odds are low that both a 6 and 10 seed win 2 games and matchup
Now last year, the Big 12 had 6 teams made it. They put 1 seed Ku and 5 seed Iowa St in the upper half in the same region (KC regional). This was a little surprising because a 1 and 5 could easily matchup in the Sweet 16
The only time 2 conference foes met in the Rd of 32 was when the Big East got 11 teams in (2011). 3 seed Syracuse and 11 seed Marquette played in the 2nd rd.