@Bramblebutter YANBU. It makes them last longer putting them in the fridge.
Even though some stuff I buy is NOT refrigerated in the store, (tomatoes, lettuce, cucumber, radishes, general salad stuff, mushrooms, potatoes, eggs, bananas, strawberries, grapes, other fruit, etc etc,) I STILL put it in the fridge when I get it.
Some 'jar' stuff, like sandwich pickle, mustard, cranberry sauce, jam, salad cream, tube of tomato puree, and similar, stays in the cupboard, but once it's opened, it goes in the fridge.