Working in Tunisian crochet makes a curling fabric because the bulk of the stitch remains on the back for a lot of Tunisian stitches. All the Tunisian designs I have done for Annie's Attic and others, including the ones sold on my website, I have designed specifically to alleviate this curling.
Try using a larger hook. With regular crochet, I usually use an H hook with Red Heart Super Saver, for instance. But, if I want to use this same yarn with Tunisian crochet, I will use at least a J afghan hook and have gone up to an L hook. You will be amazed at how well this helps with the curl. Also, Tunisian looks best and works best when it is crocheted loosely!
Another tried and true technique is to start off with a Reverse Afghan Stitch for the first few rows. This is the same thing as a knitter will do when they add purl stitches in the beginning.
You could try blocking with a light spritz of water. Or, steaming. A thick border may help as well. Try the rope border for the Personalized Baby Afghan. This is a nice thick border since you use two strands at once.
Personalized Baby Afghan: