| I can only answer as to cardio, since I don't do weights though I have read that weightlifting may increase the BS so that may complicate things.
When long distance running I find I have to both reduce insulin before and keep topping up the glucose at regular intervals. I test regularly. I also find that I often go low several hours after a very long run, even after an intervening meal.
If you're exercising for a long time and/or frequently don't underestimate its overall effect on insulin needs. When I was in training for a marathon and ran further each week I also had to cut my basal insulin. | 
