Finally, this weekend I got tribal territorial expansion to work as I wanted to. Tribal populations will migrate almost as quickly as unorganized bands, yet they will not migrate far beyond their initial region's borders. Here's an example:

To get this to work I had to make some concessions in the algorithm. Tribes will almost completely ignore bordering unorganized band populations when migrating, otherwise they would not migrate into cells that are already fully populated. I also had to tweak how frequently cell groups are updated to ignore certain factors that made tribal populations update much less frequently, and thus, migrate less often than organized bands. This has the unfortunate effect of making unorganized band migrations a tad slower. Though, the effect is minimal.

The key to get tribal populations to freely expand was to implement acculturation, which is the mechanism that allows a polity to absorb unorganized band populations within their territory, and therefore increase their prominence on each cell. Acculturation is negatively influenced by how much isolation preference there is in either the polity or the indigenous cell population. This slows down expansion of isolationist tribes, which is what I hoped would happen. Acculturation is very powerful. So without the semi-hardcoded rule that prevents a tribe from expanding beyond a region's border, a tribe would expand until fully covering any available land mass.

There's still a lot of work left to do to be done with tribal migration. Tribes are not supposed to be permanently limited from expanding beyond a region's border. They should from time to time decide to expand over neighboring regions. They also need to be capable to encroach the territory or weak neighboring tribes. But before I get to any of that, I want to improve upon the visual presentation of territories since, as you can glance from the gif above, tribal territories tend to be not very contiguous. Next week I'll attempt t patch these holes so that territories do not look that bad.