To make the cake: Lightly spoon flour into a dry measuring cup; level with a knife.
Coat an 8-inch round (thin-rimmed) cake pan with cooking spray. Line cake pan with parchment paper; coat parchment paper with cooking spray, and dust with 1 tablespoon of the flour.
Combine raisins and a second tablespoon of the flour in a small bowl; toss well.
Combine remaining flour, granulated sugar, brown sugar, baking soda, cinnamon, salt, ground ginger, nutmeg, cloves and allspice in a large bowl; stir with a whisk.
Combine oil, vanilla, and eggs in a small bowl; add to flour mixture, stirring until blended. Stir in carrot and raisins. Pour batter into prepared pan.
Remove inner pot from the Instant Pot. Place steam rack in inner pot; fold handles under rack. Pour 1 cup water into pot, and place prepared pan on rack.
Tear off a 10 1/2-inch-long piece of aluminum foil; lay foil on top of inner pot, gently smoothing it down the side of the pot. Trim pointed corners even with the rest of the foil, and tightly tuck it in under the rim.
Cut 1 (1 1/4 inch long) slit in foil about 1 inch from edge with a thin, sharp knife. Cut a second 1 1/4-inch-long slit parallel to and about 1 inch to the inside of the first. Repeat this procedure 3 times, creating 2 concentric slits in foil at intervals of 12, 3, 6, and 9 o’clock. Set inner pot inside cooker.
Close and lock the lid of the Instant Pot. Turn the steam release handle to “Venting” position. Press [Slow Cook], and use [Adjust] to select “More” mode. Press [-] or [+] to choose 1 hour 30 minutes cook time. (Cook additional time, if necessary, until a wooden pick inserted in center comes out clean.)
Carefully remove lid from Instant Pot. Blot any water that has collected on top of foil with a towel. Carefully remove foil from inner pot, so as to keep condensation from dripping onto cake.
Transfer pan to a wire rack. Lightly blot top of cake with a paper towel, if necessary, to remove any collected moisture. Cool 10 minutes in pan on a wire rack; remove from pan. Cool completely on wire rack.
To make the frosting: Beat cream cheese with a mixer at medium speed until smooth; add powdered sugar and vanilla, beating until smooth. Garnish slices of cake with frosting.