No, it won't damage your hair. I use them all the time. The only draw back is that they don't last and the color is not as "vibrant". I use the same one you're using, as well as Jazzing (same company, just that Jazzing is more vibrant) and Adore when I'm broke coz it's usually $2.00. Basically I always use gloves coz it'll stain your hands, and also I put vaseline on my forehead and ears so they don't stain. I just put the bottle upside down and squirt. I'll put on a shower cap and sit under the dryer for 25-30 minutes. Then rinse until the water is CLEAR!!! If you don't your pillows and car head rest will all be red or brown or black and you'll be highly ticked off. At this point the hair is hard. I always DC with a moisturizing co. I use humecto or Nexxus with heat for a good 20 -30 min. Then my hair is soft and supple.
You will love the way your hair looks with rinses. The only thing, like I said earlier, they only last about 4 washes (the bottle says 6) and then you have to redo it. My hair doesn't break at all with a rinse. All it's doing is coating the cuticle.