From what I've seen on other worlds, each province starts rapidly filling with barbs a few weeks in as the rim spreads out. I'm not exactly sure how they decide where people go in terms of province placement, it's different from the K's, but for me on Eremitage, it took about 3 weeks before my province went from 9 people (inactives included) to completely filled with new barbs.
On that note it took a bit longer on Bastille due to having far more people in the province, but the same result. After a few weeks it has so far always filled up. Hope I've helped a bit
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