The Plant of Curing from Isola only "helps prevent diseases on fish that are exposed to the plant." The same thing applies to the Magic Fish - they "help" (but don't totally eliminate) disease in your tanks. You can read the descriptions of the Magic Fish in
this post, which is found in the Spoilers thread of the Fish Tycoon Guides section at the bottom of the forums.
We have not seen any reports of problems with pause in "single-player" Fish Tycoon games. However, when people have more than one player, there is a potential problem. Is your friend, by any chance, playing multiple players and changing the game speed right after switching players? If so, that's the reason she is seeing time pass. If she went to the menu and changed players, then changed the game speed before she clicked Play (which she might easily do, knowing that the game had been paused while she was gone), the game will ignore that she had it paused all that time and update all of the fishies at the new speed setting when she clicks Play. In order to prevent that, you must click Play immediately after switching players if you want to preserve your game speed setting. Once you've clicked Play, you can go back to the menu and change the game speed.
If you check the other thread, your answer about the Spotanus is there!