I'm also a T2 and when I exercise (jogging) my BGs are usually about 5 to 7 points higher after exercise. However, a couple of hours later, and for the rest of the evening my blood glucose level stays a few points lower.
It was explained to me once that as we exercise we use up the glucose stores within our muscles making them want more to replace what's been used, and to do this they release a hormone to stimulate the liver to make more blood glucose - this part seems to work OK in us T2s. The higher blood glucose should then stimulate the pancreas to make more insulin.
However, T2s either don't produce enough insulin, or our muscle cells have a degree of insulin resistance, either way the increased levels of blood glucose are unable to pass through to the muscle cells, which if we're still exercising get even more depleted of glucose, and release more of the hormone to stimulate the production of even more blood glucose, etc etc (The 'Liver Dump')
The harder we exercise the quicker we use up the glucose in our muscles increasing this effect, and vice versa. Part of the 'balancing act' is finding out what levels of exercise, and for how long, we can tolerate the particular exercise without sending our blood glucose through the roof.
This will be different from person to person as we all have different abilities to produce insulin, or have different levels of insulin resistance.
Our most famous olympian, Steve Redgrave, is also a T2 and to be able to exercise at the extremely high levels he was doing he went onto an insulin regime under medical supervision.