Preheat oven to 375°F. Line a 12-cup muffin pan with liners and lightly mist with spray.
Whisk flour, baking powder, baking soda, and salt in a medium bowl.
Stir cream cheese with 3 tbsp granulated sugar and 1 tbsp lemon juice until smooth; set aside.
Toss raspberries with a teaspoon of the measured flour to lightly coat; reserve a small handful for topping.
Whisk melted butter with remaining sugar, eggs, vanilla, buttermilk, lemon zest, and orange zest until combined.
Fold dry ingredients into the wet mixture just until no dry streaks remain; avoid overmixing.
Gently fold in most of the raspberries, keeping a few aside for the tops.
Spoon batter to fill cups about halfway. Add a small dollop of cream cheese mixture, then cover to about 3/4 full.
Sprinkle with turbinado sugar and nestle a few reserved berries on top.
Bake 20–22 minutes, until golden and a tester comes out with a few moist crumbs. Cool 10 minutes, then transfer to a rack.
Whisk powdered sugar with 2 tbsp lemon juice until smooth. Drizzle over cooled muffins before serving.