Hi Marcade, I just downloaded the png for this tileset and opened it in Paint.NET. the transparency is correct. If you open the file in MS Paint, I don't think it preserves the transparency, so that might be the issue.
Thank you for your support and let me know if there's anything else I can help with!
The tiles should be placed in B, C, D, or E, not any of the A tiles (those are autotiles, a special type).
If you opened the tiles in a program that affects the alpha channel (transparency) and then save the tiles, you may have lost transparency. Just try downloading again and importing directly into your game.