Insulin is like the key to a lock in your body. It allows your cells to take in glucose. Without it the gluc stays in your blood and your body 'thinks' it is starving (one reason appetite tends to go up, yet you loose wt as a symptom of the condition)
There is a something called the "Somogyi effect." This is a natural way for your body to react to a low blood glucose. When you get a low BG your body uses a hormone called glucagon to raise it. It involves release of sugars from your liver. This is a safety mechanism for the body; but much slower reacting than insulin release from your pancreas.
It could be your BG dropped quite a bit during the night and your body reacted with the above; however, the over-swing is usually quite marked. Sometimes your body wakes you up during the night if your BG drops low (not always though). I would approach your diabetic team again as increasing the insulin may not be the way fwd.
Out of interest, and tell me to ****** off it too personal, but how much do you weigh? I know in vetmed we usually aim for 1/2IU per Kg BW (acc to my endocrinologist its much the same for humans). However, this does vary with sensitivity to insulin.
D