Yup totally normal. The exercise or level of resistance that causes this may be different for all, but the reaction you experienced is (or should be) experienced by all. It means you are giving a max effort.
If someone never experienced this, they have never given a max effort and they have cheated themselves. Look at the huge weight lifters in the Olympics. See the shaking they do. We all have our limits. Just make sure that when you force yourself to do those extra reps and hold those stretches that you are not breaking proper form or experience real pain (as opposed to discomfort) because this will lead to injury. Concentrate on doing you most at proper form first. Giving the max effort with proper form is the ideal. However, when going for max effort be aware that there are some exercises that you should not try this without a good, experienced spotter. I don't want you to go off and try to get that same feeling while doing a barbell chest press. This can be very dangerous. Without a trusted spotter, and sometimes even with one, just aim to go to near failure instead.
It will get better as your strength improves and the great news is that it will be quicker than you are probably thinking. To get the benefit of strength training, however, you need rest and recovery. That is when the true gains in strength come. Make sure you don't do the same DVD or work those same muscles again the next day. You can do a DVD training different body parts the next day or if you worked the full body on one day, just take a cardio only day the next day.