Relative humidity is the ratio of the amount of water the air is holding to the amount of water the air *can* hold. So if the air can hold 100g of water and it is currently holding 90g of water, then the relative humidity is 90%. As the temperature drops, the amount of water the air can hold also drops. So you can imagine that at 30 C the air might be able to hold 200g, at 20 C it might be able to hold 100g and at 10 C it might be able to hold 50g (I just made up those numbers -- probably not even close, but hopefully it will help you understand).
Let's image that we have summer air at 30 C (which can hold 200g) and the relative humidity is 25%. That means that the air is holding 50g of water. If we cool the air down to 20 C, then the relative humidity will go up to 50% -- the air can hold 100g and it is still currently holding 50g. If we cool it down to 10C, then the relative humidity is 100%. The air can hold 50g and it is currently holding 50g. If we cool it any more, the water will condense and drop out.
Now, imagine your refrigerator. The air is something like 13C. You have 90% humidity. Let's imagine that it can hold 60g of water and is currently holding 54g of water (90% of 60 = 54). How do we keep the refrigerator cold? We do it by having a compressor cool some liquid and then run that cool liquid along the back wall of the fridge. The liquid has to be colder than the air in the fridge because that's how we extract heat from the refrigerator -- the air in the fridge heats up the liquid, and in turn gets a bit colder. The liquid is pumped to the outside of the fridge where the heat escapes and then we pump it back through the compressor to cool it down again. It is literally a "heat pump". The liquid takes the heat from the inside of the fridge and is pumped outside (that's why the back of your fridge is warm).
Now imagine that the liquid that we are pumping along the back wall of the fridge is 10C. It cools the back wall of the fridge to 10C. This keeps the fridge at an average temperature of 13C. But there is a problem. The relative humidity at 13C is 90% (it holds 54 grams of water and *can* cold 60 grams of water), but the relative humidty at 10C will be 104% (it holds 54 grams of water and *can* hold 50 grams of water). The excess water condenses on the wall of the fridge and runs down to the bottom.
To combat this, most modern fridges have built in dehumidifiers that constantly try to keep the humidity at 70%. This is one of the reasons why modern fridges are difficult to use for this application -- the fridge will constantly be working against you. But even if you manage to get the humidity up to 90%, you will have a pool at the bottom of the fridge. Fridges are just not good for this application.
Walk in cheese cellars are made using air conditioners instead. They blow cold air into the space. This means that the walls are always warmer than the air which means that you don't get any condensation on the walls. The air conditioner will get condensation, but it's easy to drain that.
One thing that may help is to try to set your temperature range in the fridge and the humidity such that the temperature of the back wall gives you a humidity below 100%. The problem with that is that you will probably have to run the compressor *a lot*. Basically, what you do is give the temperature controller a very narrow range of temperature so that the back wall is not much colder than the air and then dial back your humidity to 85% or something. But this means that the controller is going to toggle the compressor on and off again very rapidly and it will eventually burn it out.
Maturation boxes is the answer. Or a walk in cellar cooled by air conditioners.
