Bananas should not be kept refrigerated because of the enzymes that the bananas contain.
When the enzymes in the bananas become cold they become inactive which can cause the bananas to not ripen properly and can cause skin damage to the bananas.
Hot climates are where bananas grow and they are not used to the cold temperatures so they also get cold shock from the cold temperatures.
Whenever I tried putting bananas in my refrigerator it also made them too mushy and although they were still safe to eat the bananas didn't taste as good as they did when fresh without refrigerating them.
Bananas will ripen more when at room temperature and when you put them in the cold refrigerator the bananas will not be able to naturally ripen and will usually turn mushy.