You should actually change colors on the last stitch of the row below. I don't have the pattern, so I don't know what stitches you're doing, but here's a (hopefully helpful) explanation: You want to add the new color at the last YO and pull through of the stitch. So, if you're doing single crochet, you put the hook through the stitch, then pull the new color through. If you're doing double crochet, start with your first color, YO, put hook through, YO (old color) and pull hook through two loops on hook, YO (New color) and pull through two loops on hook.
Leave a fringe-length tail of both colors.
If you need clarification of this not-so-concise description, let me know!