Yes blackberries should always be kept in the fridge to keep them cool and prevent them from going bad.
If you plan to eat the blackberries within a few hours of buying them or picking them then they are safe to leave out at room temperature.
But if you don't plan to eat the blackberries within a few hours you should always refrigerate them to prevent spoilage of the blackberries.
Also never wash the blackberries until you're ready to use them or eat them because washing the blueberries too soon can cause mold to grow on the blackberries.
When refrigerating store bought blackberries you should always keep them in the original container.
Eat the blackberries within a few days to prevent spoilage of the blackberries.
Blackberries can last up to 6 days in the refrigerator but it's best to eat them within a few days for the freshness.