For the rhubarb jam: Toss the rhubarb with the cornstarch in a medium saucepan. Stir in the sugar and water and bring to a simmer over medium-high heat. Reduce the heat and simmer, stirring often, until the rhubarb has broken down and the mixture is very thick, about 20 minutes. Cool completely.
For the crust: Place a large rimmed baking sheet in the oven and preheat to 375 degrees F. Line an 8-by-8-inch metal baking pan with foil; butter the foil.
Pulse the flour, sugar and salt together in a food processor. Add the butter and pulse until the mixture resembles coarse meal. Add the water and pulse until the dough comes together in a ball.
Measure out 2/3 cup of the dough and place in a small bowl. Transfer the remaining dough to the prepared baking pan and push evenly into the bottom of the pan. Refrigerate until firm, about 10 minutes.
Meanwhile, add the oats, allspice and cinnamon to the dough in the bowl and mix well to combine. Refrigerate until firm, about 10 minutes.
Spoon the rhubarb jam onto the chilled crust and spread evenly with an offset spatula. Crumble the oat topping over the jam. Place the baking pan on the preheated baking sheet and bake until the crust and topping are golden brown, 40 to 45 minutes. Transfer to a rack to cool completely. Carefully remove from the pan and cut into bars.