I find the same when I exercise, though I peak a later sometimes an hour or two, (in australian terms
from about 6.0 (100ish) before exercising, to about 14 (~250) or more. If an evening exercise session, I have normal dinner, normal insulin, and it comes down all by itself overnight to below 6.0 again in the morning - even sometimes a hypo. My Doc says its normal too, but I still feel the high sugar!
I am experimenting with jabbing a very small dose before exercise (like 1 unit) with a few jelly beans - me thinks it may ease or stop the body having an 'energy crisis' on/during exercise, and prevent/reduce the spike from gluconeogenesis?