To add normal map to the tiles, you shoud open the tileset, select in the tile editor the tile to which you want to add the normal map, and then add the normal map in the inspector, under the "selected tile" group.
There are some considerations to have. If you create tiles from sepparate image files, then you add the corresponding normal map to each one.
If you create single tiles, but all from a single TileMap image which includes all the tiles, then you have to add the normal map to each tile, but that normal map should be the normal map of the complete TileMap, not just the normalmap of the selected tile. And yes, you will end up adding the same normal map to each individual tile in this case.
If you use autotile, you just need to set the complete normal map once.