Hey Amora,
The "Outside - Custom" is the slightly modified tileset I created for this tool. Right now I think the only difference between it and the standard "Outside" tileset is the desert sand textures (I eventually wanted to add other things such as snow tiles which aren't in the standard tileset). If you switch it to the regular "Outside" tileset things will still line up, but the desert sand where wild pokemon can spawn will probably be missing. Oh - and also the left/right facing stairs.
Did you do these 2 steps from the readme?
In the Tileset folder, there are 2 files which should be moved into your RMXP project folders:
OutsideCartographer.png should be placed in <your project>\Graphics\Tilesets
Tilesets.rxdata should go in <your project>\Data folder, overwriting the existing file.
Note that the Tilesets.rxdata will overwrite any tilesets you currently have in your project, so it's recommended to be done on a fresh Essentials copy. You can manually add the custom tileset a different way if you prefer (without copying Tilesets.rxdata), but then you'll have to set up all the permissions etc. Also, I put the tileset in slot "025" and the generated maps will reference this, so if you didn't copy in the Tilesets.rxdata and had it manually added in a different spot, that might explain why it was funky.
Just for reference, the tileset sits here in my test project: