Yes, because you do not turn your work around to start the next round, the working yarn will be coming from what seems to be the wrong side of the work. You need to pull the first stitch or two nice and tight, and it will appear that you will have a horizontal strand of yarn going across the back of your cord, but if you pull the first couple of stitches tight enough and keep going for quite a few rows, you will see that it will begin to form a tube and those strands will not be noticeable at all.
That said, 6 stitches sounds like quite a few to use for an i-cord. I don't think I've ever done more than 3 or 4. Is this is what's instructed in a specific pattern?