Okay...i think i know whats going on. But its kind of difficult to explain.
I think Construct "blurs" the edges of the Tiles a little bit, so if your Tile is surrounded of white, the Tile will show a white line around it. If you put your Tile next to a Tile that looks similar, it "blurs" into this tile but you cant see it because of the similarities.
I saw stuff like this years ago in the Textures for 3D models.
Edit:
Its basically this:
One way around this is coloring the Background (of the Tilemap) in a similar Color like the Tiles on top of it.
So even if the Tile "bleeds" into the color around, its a similar color, so not as much visible.