Tartan cloth does have a "right" side and a "wrong" side, the wrong side being where you will find any knots, etc., from where threads were joined and so forth. So you will want the kilt made with the right side facing outward, so any imperfections like that will be hidden. What this usually means is that the twill line runs up and to the wearer's right, when worn.

For whatever reason, sometimes mills weave cloth with the twill running opposite. For example, Lochcarron's strome range has the twill running in the opposite direction than the norm. This is why when I make kilts from Lochcarron cloth (such as Tobus's four yard box pleated kilt) the twill will run the opposite way.

Some kilt makers will use the other side of the cloth in these cases, because they were taught that the twill should go in a certain direction. And that's understandable. However, the reason why they were taught that has nothing to do with the twill direction per se, but rather the need to put the right side of the cloth on the outside of the kilt, in order to hide any flaws.

Now, as it so happens, most of the time the flaws on the "wrong" side of the fabric are pretty minimal and sometimes non-existant, depending on the particular length of cloth you happen to be working with. So what side is facing out on the kilt is pretty much a non-issue.

But there you have it. If I had a kilt with the twill running in the opposite direction as normal, I wouldn't really give it a second thought. It could be that there was an issue with the other side of the cloth so that the kilt maker did it that way intentionally. Or it could be that the "wrong" side of the cloth was so indistinguishable from the "right" side that the kilt maker made the mistake of putting the wrong side on the outside of the kilt, in which case if he/she couldn't tell the difference, why worry about it! :-)