I'm having trouble picturing what you're describing. What does the jig look like? Also by "on its side", do you mean the wide part of the side, or the thin? I was taught to sharpen the tool with the wide side flat on the platform, 90 degrees rotated from what is being done in this picture (obviously, my tool has a flat profile -- I wouldn't be able to lay a diamond cross-section tool flat on the platform):
Attachment 347204
To ensure I don't get a point with a skewed end on it, the platform has to be square with the part of the wheel the tool is contacting. I can get it close eyeballing it, but it always seems just a little bit off.