15-20 percent is customary
If someone other than the stylist washes your hair, about $2-5 is customary depending on the type of salon you're going to (low-end versus high-end).
At the end of the day, you want to tip based on the services given so if you feel that 15-20 adds up to a lot, remember to not tip on the tax or on the product but only on the style price itself.
So if they are putting the cost of the dye in there, only tip on the dying process cost itself.
Thanks for your help. I appreciate all the extra information.