Having said that storage instructions for Parmesan are pretty much unique, wait till you hear the ones for mozzarella. They might seem plain crazy.
Depending on which dairy you go to in Campania, instruction on storage temperature can range from 4°C–22°C.
Shelf life too can range enormously. Even amongst the smallest dairies it can be anything between 3–15 days. In larger dairies where they use pasteurised milk and preservatives it can be 4–6 weeks.
So that people don’t get confused, we recommend keeping the mozzarella somewhere cool (our dairy suggests 14°C) and eating it as soon as possible.
If you are going to keep it for any length of time (the mozzarella we sell at Borough Market has 9 days on it) then store it in a fridge.
The texture of mozzarella stored in the fridge will break down over time, so eat it as soon as possible. Most importantly, serve it at room temperature by placing the container in hot water for 15 minutes before eating.