Yeah, I have the same issues and I see it is the major issue. Is there someone who can develop a tutorial on how to select your drawing field? I was wondering if maybe they may be able to set a defined line on the tiles so when we dowload them it is clearer where we need to draw the line to select the area. Like make it a definate line that appears as red and green dots or candy cane dashes so we can trace over that line when we select the area to make a layer of our drawing field???? I know I select the area repeatedly sometimes trying to deside if I am on the line or on one side or the other. It's become like a hit and miss thing, I keep my fingers crossed and fire.

What drawing program are you using? If it's photoshop you should be able to create a square selection by using the 'fixed' option. Then you just plug in the dimensions of your tile and zoom in to line up the one edge. I would think that other programs would offer a similar option.

Probably you are creating a new layer for the 128x128 tiles you're about to draw, and then use some kind of smooth/smear tool near the edges, which makes some transparency smear from the edges over to the actual 128x128 image, and then when you flatten it it will merge with the background layer and become black. Dunno if that made any sense.
Anyway, a good solution is to draw outside of the 128x128 region, on the squares/don't draw here bit, on the sides which do not yet blend to another tile. It will be cropped off when you upload it, and no black borders.