What does "set aside for x hours" imply?
You leave it at whatever temperature is adequate for the food (or stage of food) that is left aside. 

If you are canning your chutney, then all stages before going into the canner need refrigeration, and all stages after getting out of the canner are safe at room temperature. So, if the recipe wants it to be done before canning, you have to put it in the refrigerator. 

If it is after the canning, there is a twist. For most shelf-stable foods, there is nothing wrong with leaving them in the refrigerator instead of outside. But if the "leave aside" step in your case comes immediately after canning, then its purpose is to ensure the proper seal. For that, you should best leave it under the conditions that it will be exposed to in the long term, that is, outside.