Hi, Christie! IMHO, I do think it is normal to feel your back a little more after doing KPC, especially if it's your first kickbox routine. Many of the movements in KPC incorporate trunk-twisting, and bringing one knee up and across the body to the opposite side while at the same time performing that "knee smash". Also, you're working the legs a great deal from the hip joint with the front, side and rear push-kicks as well as roundhouse kicks.
IMHO, as fine a workout as KPC is, it should not be done more than once per week precisely because of the implications to the lower back. Make sure to keep current with your core work as well (and KPC just happens to have an awesome core and ab routine incorporating the stability ball) with routines that utilize plank work, traditional supine crunches for the rectus abdominus AND the obliques, supermans etc. If you don't have the Pyramid Upper / Lower Body DVD consider getting that, not only for the entire workout but also for the PUB ab routine; also consider getting the Boot Camp / Muscle Endurance DVD; the ME workout has a great ab routine as well.
HTH -
A-Jock