Fermented Foods do not require any refrigeration however if you want to store the fermented foods in the refrigerator you can do so.
But it's not required to store or keep fermented foods in the refrigerator.
As long as you've fermented the foods properly and canned the fermented foods properly they can last a year or more before going bad.
After you open the fermented foods after canning then refrigerating them would be a good idea to keep the fermented foods from growing any bad bacteria that could make you sick but as long as the fermented foods remain sealed before consuming they are very safe to eat without refrigerating them.