Combine cherries and granulated sugar in a medium saucepan over medium heat; bring to a boil. Reduce heat, and simmer 10 minutes, stirring occasionally. Combine cornstarch and 2 tablespoons water, stirring until smooth. Add cornstarch mixture to cherry mixture; bring to a boil. Cook 1 minute, stirring constantly. Remove from heat; stir in rind and almond extract. Cool.
Preheat oven to 400°.
Combine 3 tablespoons powdered sugar, cheese, and vanilla in a small bowl, stirring until well blended.
Place 1 phyllo sheet on a large cutting board or work surface (cover the remaining dough to keep from drying); lightly coat with cooking spray. Repeat layers 3 times. Gently press layers together. Using a sharp knife or a pizza cutter, cut each phyllo stack lengthwise into 4 (9 x 3 1/2-inch) strips. Spoon 1 teaspoon cream cheese mixture onto 1 short end of each rectangle. Spoon 1 level tablespoonful cherry mixture on top of cream cheese mixture, leaving a 1-inch border. Fold 1 corner of edge with 1-inch border over mixture, forming a triangle; continue folding back and forth into a triangle to end of strip. Repeat procedure with remaining phyllo, cooking spray, cream cheese, and cherry mixture.
Place triangles, seam sides down, on a large baking sheet coated with cooking spray; lightly coat triangles with cooking spray. Bake at 400° for 10 minutes or until golden. Cool on wire racks 5 minutes. Combine the remaining 5 tablespoons powdered sugar and juice in a small bowl, stirring until smooth. Drizzle juice mixture over turnovers.