Since my crochet skills are so very limited (this is only my second project), I can't say for sure, but I think that is what I did. I read somewhere (I've been all over the net today!) that you should add color on the last stitch of the round before you start the new round.
So on the last stitch of the brown round, I added the color (pink) on the last loop before I pulled through for the SC (so the last crochet stitch still was brown, but the loop on the hook was now pink and ready for the first stitch in the next round).
Did I do it correctly? It looks exactly like the 'stacked spiral' when knitting in the round (if you don't do the jogless join). However, I may be making too big of a deal out of it because there will be a ruffle added on that row after the purse is finished, so it will cover it up somewhat. I just want to do the best that I possibly can since this will be a gift.