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You are correct that osmosis will occur when watermelon (or any fruit pieces) are put into distilled water. Osmosis is the process of water going across a membrane from an area of higher concentration to lower concentration. The watermelon piece has a lot of sugar (and other chemicals and ions) dissolved in it, so the pure water will be drawn into the fruit to try to even out the concentration gradient. The fruit should swell with the added water intake. But given enough time, the fruit fibers will break down and lost their structural rigidity. When this happens, the water and other chemicals in the watermelon will no longer be contained and are free to seep out into the distilled water container. When this happens, the sugar diffuses into the larger mass of water and the watermelon loses mass. So the other process at work here is diffusion.
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