Indeed it sounds like you have your isometric graphics cut up in too small pieces, which won’t line up when placed on the isometric grid. You need to make sure that when adding your tileset, you choose a tile size that does not cause tile graphics to be cut into pieces. In this, isometric maps are different from orthogonal maps, where this problem does not exist.
Maybe the following howto can help as well:
You just need to keep in mind that when your tiles are bigger, you need to choose a bigger tile size when adding the tileset.