First, there are so many people (male and female) who enjoy intense stimulation to their nipples that there's a slang expression for it: "tit torture," also referred to as TT in personal ads of the naughty sort.
Normal is a meaningless term. Sexologists simply don't have enough hard data to make an accurate scientific judgment about what is normal. In COME HITHER, I differentiate between "acceptable" and "unacceptable" sexual behaviors. If someone enjoys something in bed, and finds a partner who is happy to participate, and both are consenting adults, my opinion is that it's a good thing. Whatever keeps a couple's intimate life vibrant is good in my book.
So, yes, it's fine for him to want an intense level of pain to his nipples. It's unlikely that with your fingers alone you can do real damage. Extended nipple clamping can sometimes produce nerve damage, so if you use clamps or grip your fingers on them for long periods, make sure the nipples don't go numb (a first alert). If the play includes scratching or otherwise causing the nipples to bleed, you must treat it as any open wound and take care to prevent infection. If you actually tear tissue, consult a doctor.
It doesn't surprise me that he only likes pain to one specific area of his body. Just as some spanking fetishists will only accept pain to their buttocks, and some foot fetishists are only aroused by tight, painful shoes, some people just think nothing's sexier than nipple pain.
If you are really disturbed by this activity, for whatever reason, you have the right to turn him down or set limits on how far you'll go. But if knowing it's a common and acceptable behavior reassures you, then have fun with it. Perhaps there's something unusual you'd like him to do for you? Under the criumcstances, tit for tat seems only fair.