Car Jumps on shifts

Each time I turn my car on and put it into gear it jumps. It doesn't matter if it's a cold start or not. The only issue is that it jumps when it is turned on and put into gear. I was afraid it could be the transmission but I am taking it in for service and when I called the dealership the guy said it is highly unlikely for a car that only has 12,200 miles on it to have a transmission go bad. That is despite the fact that it is 7 years old. He said a car with such low miles shouldn't have a bad transmission. What might the problem be?