Speculation. Mostly because, at least to my knowledge, the Sona were never in the Delta Quadrant where the Dominion was. Dialogue says the Baku had been on that planet for a long time, even before the Dominion War, and the feud for a long time before the Federation got involved with.
So that leads me to believe that the Sona and Baku are natives to the Alpha Quadrant.
Hmmm.... now I'm wondering if that could have actually been the original source of the feud: the white being made for a tyrannical government power.
No.
The Dominion had forces in the Alpha Quadrant when Sisko mined the wormhole, effectively cutting off the Dominion from supplies and reinforcements. The Dominion set up facilities to make Ketracel White in Cardassian space, but Starfleet was especially eager to destroy those facilities. Meaning they would need third-party suppliers to make the drug. Plus a third-party with no conflict with the Federation would be unlikely to be attacked. Even if they were making White.
The S'ona seem like a no-brainer since they were already committing heavy resources to health care to keep themselves alive. It was probably easy to convert one of their facilities to make White.