It sounds like you are probably experiencing the Last Meal Effect.
It is very common, and isn't anything to do with type 2 diabetes. It happens to non diabetics too if they cut their carbs and keep them low.
This link explains it better than I can.
http://nutritionwonderland.com/2010/05/understanding-our-bodies-insulin/
This is an extract from the Regulating Insulin section:
Once we start to eat, our bodies ramp up insulin secretion, in what is often called first phase insulin release. Insulin that was kept in storage while our blood glucose levels were normal is released all at once, leading to a dramatic increase in insulin levels. The amount of insulin secreted in the first phase response to a meal is determined by the amount of glucose encountered in the previous meal – the more you needed last time, the more is released in this first phase. In a healthy person, this first phase response peaks a few minutes after you’ve started your a meal.
The β-cells then take a quick pause. If the first pulse was enough, then they slowly take up the insulin they released, and store it for the next meal. If the blood glucose levels stay high, though, the β-cells begin producing and releasing insulin in pulses every ten to twenty minutes. They continue this until the body’s blood glucose gets back to normal levels. The blood sugar rise caused by the meal peaks about half an hour after eating, and this, in turn, leads to a decrease in insulin production and release.
So your body has insulin stored ready for use based on the amount you required for the last few meals you ate. But if you present it with increased carbs in a meal, it is not prepared, and it takes a while to ramp up the insulin production to deal with the unexpected glucose levels. It still gets there, but it may take an hour or two rather than 20 minutes - which is why we see the exaggerated rise in blood glucose when we eat extra carbs on our low carb diet.
But the important thing to remember is that it is temporary, reversible, and it you maintain the increased carb levels, your body adapts within a few days.
To avoid the issue, you just increase carbs for several days, so that your body adjusts to the new insulin demands, and then the Last Meal Effect adjusts to your new, higher carb level.