Not sure where you're located and what your local code is, but the NY State IRC (International Residential Code with minor modifications) prohibits notching in the middle third of the span. That 8" puts the notch in the middle third.
The depth of the notch, if it wasn't in the middle third, is of an acceptable depth - depth of notch/6 = 1.5"
It's not a great situation. You may never have a problem, but your contractor damaged your house and it doesn't conform to the IRC. Ask him what he's going to do to strengthen the weakened joists. Sistering a 3-4' 2x6 or 2x8 under the notch would stiffen the localized weakness. The added pieces should be glued and nailed.
Generally, whenever an electrical or plumbing line is run perpendicular to the joists it should be drilled instead of notched. It doesn't weaken the joist as much and keeps the line away from the face of the joist, thereby preventing someone inadvertantly hitting it with a nail.
R