Make the rice pudding: Combine the rice, coconut milk, water, vanilla extract, sugar and a pinch of salt in a rice cooker. Stir then cook according to the manufacturer's instructions, until the rice is fully cooked and the liquid has been absorbed, 25 to 30 minutes. (Alternatively, cover and cook in a heavy-bottomed medium saucepan over medium-low heat until the rice is fully cooked and the liquid has been absorbed, 25 to 30 minutes. Stir frequently to prevent the rice from sticking.)
Remove from the heat and let stand.
Meanwhile, make the fruit salsa: Combine the mango, strawberries and lime zest in a medium bowl. Stir and let sit for 15 minutes. This gives the flavors time to marry together.
While the rice pudding is still warm and steaming, top with the fruit salsa and serve. (See Cook's Note.)
The rice pudding can also be enjoyed cold but I prefer it warm. There is something more comforting about it.