See? To prevent that, when doing intarsia on a vertical join, twist the yarns of the two colors together on the wrong side of the fabric. You will twist the yarn every time you do a color change, but all the twisting is done on the wrong side. Here is a little photo tutorial on how to do that:
I have shown the wrong side of the fabric to make it easier to see, but you twist the yarns the same way if you are knitting on the wrong side.
I have knitted the four buttonband stitches in dark blue and now want to pick up and knit the aqua stripe.