What Talavaj referred to is a general issue of texture atlases, nothing related to Warcraft 3, which is called pixel bleeding, if you want to research it.
The common solution is what Talavaj suggested - padding the boundary with duplicated pixels (with access to code, you could fix this without the need for people to mess with their textures, but we don't have access).
However, as far as I can tell, your tiles aren't correct in the first place. This is pretty obvious, seeing that some wrongly sampled pixels won't make such a big noticeable effect.
I am not sure what the problem is, but it probably has to do with the alpha channel.