Prepare cake mix according to manufacturer’s directions in a 9x13-inch baking pan. Place evaporated milk, condensed milk, 1 cup cream, and ¼ cup rum in a saucepan; bring to a boil over medium heat. Lower heat and simmer 10 minutes; cool.
Invert cake onto a rimmed baking sheet. Using a long-tined fork, poke holes all over cake; pour half of milk mixture over cake and allow to sit for 30 minutes. Place baking dish over cake and carefully invert cake back into pan. Pour remaining milk mixture over cake, cover, and refrigerate for 3 hours.
Whip the other cup of cream with remaining rum and sugar to soft peaks; spread over cake. Garnish with cherries and mint leaves. Cover and refrigerate until ready to serve.