I'll state first that I'm a T2, so what I say may not be entirely relevant to T1.
However, my experience based on fingerprick tests is that my BG readings increase due to stress, be that the physical stress of exercise, or psychological stress. It causes your liver to dump glucose into your system, which is a physiological response to give you the additional energy needed to handle the situation.
The liver's response is unavoidable for all of us. Some T2s are on medications that can reduce the liver's output of glucose, but it still happens. For a T1, I would assume you'd need to somehow dose with insulin, but I have no idea how you'd go about that, or how to calculate based on an unknown carb load from a liver glucose dump.
@Antje77 has done some testing and experimentation with exercise, how it affects BG levels, and has experience dosing insulin for it, so will be able to offer better insight than T2s on the matter.