Your body can store about 2000 calories worth of glycogen to use as energy reserves. About 1500 of that is stored in your skeletal muscle and cannot be transferred to other parts of your body. The other 500 is stored in your liver and can be released whenever and wherever needed.
Unfortunately, when our body THINKS we need it and when we ACTUALLY need it aren't always the same. Our livers can "Dump" glucose in the morning which is why many of us have elevated morning blood sugar levels (dawn phenomenon).
With exercise, our bodies can exhibit similar behavior and it's important to understand how your body reacts to specific types of exercise.
The two most common types of exercise I do are heavy weight lifting and short distance running (3-6miles at a time) at a pace of about 6-7mph.
Heavy weight lifting does not provoke a blood glucose spike for me and I'm extremely sensitive to insulin after heavy weight lifting. My blood sugar will rapidly drop 30-60 minutes after a weight lifting session.
Running is a bit different for me. As soon as I start running, my blood sugar spikes as my liver begins sending its stores of glucose to my blood. Eventually, I deplete my liver's glycogen reserves and my blood sugar starts to fall (usually after about 30 minutes of running). Furthermore, I find that my fasting glucose levels are about 1-1.5mmol/l higher on the days I don't workout (assuming I take the same amount of insulin).
Remember that your body won't always burn 100% glucose or 100% fat (ketones). Generally speaking, your body is more likely to burn glucose when your heart rate is significantly elevated because it's a quick source of energy. Your body would generally burn fat in lower heart rate situations . That's why you may see bodybuilders walking on treadmills rather than running. The idea is to burn as much fat as possible and retain as much glucose/glycogen.
Again, everyone is different and there are many other factors that can affect how your body responds to exercise. I'm 27 years old and in fairly good shape so my body doesn't seem to realize walking is an exercise. Consequently, I have no blood sugar changes as a result of walking while many others may.