In your palette, the first 6 rows require a specific color arrangement so that sprites show up properly. See the palette section in Disguise's Tileset Resources.

I'm not sure how well you know TilesetPal, so I'll give a mini tutorial. Go to Palette -> Merger to use the Palette Merger. From there, load the palette named Jazz2.pal which comes with TilesetPal (located in the Palettes folder). Select the first 6 rows in the External Palette and press the arrow point to the right then press OK. In the palette on the main screen, you'll have to change what certain indices are marked as. The indices that I will now mention correspond to the Index you see at the bottom-right corner next to the Color Picker.

Indices to mark as Don't Change:
1, 15-55, 59-95

Indices to mark as Don't Use:
0, 2-9, 246-255

When you're done, you should have a palette that looks like this:



In this example, the purple color in index 1 should be used as the transparent color. You can now use Reduce Colors, or you can add one extra step and adjust the palette for a textured background by using a similar method.