Tell me if I'm seeing things:

In fierce combat with the Yor, I found that the 3-movement restriction in their space was really cramping my style. No problem, I thought, I'll just take some planets and extend my cultural borders into their territory. So I took two worlds by their lonesome between our territories. The next turn, those borders had not moved. The turn after, they started to recede at a creep. It was many turns before my influence had extended to cover my two new worlds.

I'm guessing this is a feature, "influence creep", to show how the change is not instantaneous. I like it. It's especially crucial for the Yor!

Another note: this process did NOT apply to Homeworlds: when I took the Thalan and Drath homeworlds, the borders shifted immediately.

Incidentally, after buying peace with the Yor, I now control two-thirds of the galaxy and will soon launch the final war. The Yor, perhaps sensing that my war machine was rolling over everyone else, declared war on the Drath to in an effort to expand and deny me that territory. Devious!