This is not normal behavior of a typical mechanic. Most mechanics/shops will still continue to charge their normal hourly rate no matter if you bring in the parts or if they get you the parts. The only difference is, they will not warrant the parts you bring in.
You may want to look at the fine print of why they are charging the extra $15/hr. If the reason is to warrant the items you bring in, then the charge may be equitable. I don't see any other reason for the extra charge.
Zach is right in that they will make money from you any way they can. Most shops, whether a chain or local, do not supply their own parts. They farm out and around to get the cheapest parts available. Some will have deals made with a certain parts supplier to get their parts at a discount. This is a business-to-business transaction which works well for both of them. Some shops will not mark up their parts, but others do. For instance, I had a female friend whose van was not running right. She took it to a shop and had them look at it. They quoted her a price of ~$900/parts & ~$1000/labor to do the repair. I did some research to figure out what was going on (which they totally missed the diagnosis, btw) and figured out I could purchase the needed parts for ~$300. I double checked their price quotes on parts for what I could find them for. Every last part was two to three times more. I asked them why the difference. They said they marked up the prices to warrant the parts. I asked them why if the parts houses already provide warranties on all the parts. They had no answer for me.
Bottom line: if a shop won't let you find your own parts, find a different shop (or learn how to do the work yourself ;-).