Should tiles of "stones" be removed from the backing?
Mosaic stone tile is supposed to be installed still attached to its mesh backing. Otherwise it would be more efficient to go to a landscaping company and buy a truckload of river rock.

From what I can tell, there could be two causes for the 'line' effect you ended up with:


The mesh squares were poorly designed/manufactured with all the stones lining up to form a perfect edge along the sides. There's not much the installer could have done to counteract this.
The installer didn't take time to make sure the edges appeared natural when lining up the mesh squares. It may also be very difficult to tell this effect will occur prior to applying the grout.


My guess is that it's most likely a combination of these two factors.