Pat watermelon cubes completely dry with paper towels and place them on a parchment-lined plate. Freeze for 20 minutes while you prepare the mochi dough.
In a microwave-safe bowl, whisk together sweet rice flour, sugar, and salt until combined. Add watermelon juice and vegetable oil, whisking until the mixture is completely smooth with no lumps.
Cover the bowl with plastic wrap and microwave on high for 2 minutes. Stir vigorously with a wet spatula, then microwave for another 1 minute. The dough should be translucent and stretchy.
Dust a clean work surface generously with potato starch. Transfer the hot mochi dough onto the surface and dust the top heavily with more starch to prevent sticking.
Once cooled to just-warm temperature (about 5 minutes), divide the dough into 12 equal pieces using a bench scraper. Flatten each piece into a 3-inch circle with your palm.
Place one frozen watermelon cube in the center of each circle. Gather the edges up and around the fruit, pinching firmly to seal. Roll gently between your palms to smooth the seam.
Dust off excess starch with a soft brush and place each mochi seam-side down on a parchment-lined tray. Refrigerate for at least 30 minutes before serving to allow them to firm up and the flavors to meld.
