It's not a stupid question....
There are many causes of fin rot. But if it's an active infection, then it's likely caused by bacteria in the water.
Since your guys are in a divided tank, the same bacteria will be on both sides of the divider.
BUT in most cases, it needs a way to enter the fish. Entrance can occur through cuts or abrasions. For example, if the fins are torn, they can develop an infection.
The best way to control this is through increased water changes. Frequent water changes will remove toxins and bacteria from the tank. This will lessen the chances of a fish developing an infection from bacteria in the water.
Another good way to help prevent infections is by providing good nutrition. Quality food will keep the fish healthy. This will give them strong immune systems, which can fight off infection better. Look for quality high-protein ingredients in their food. This will give them the nutrients they need.