Exercise is weird with T1.
I often find that an activity like running will make me spike, but then I gradually come down if it's a fairly lengthy one.
Swimming doesn't make me spike (unless it's short course sprints). The same with cycling.
Lucozade to treat hypos is no myth, it's very effective as is any carbohydrate drink over a food. It's absorbed faster in liquid form.
It's common to have hypos hours after exercise, it's to do with a mixture of increased insulin sensitivity caused by the increased efficiency of the GLUT4 transporters (the means in which glucose enters your muscles) and the replenishment of your liver's glycogen stores.
To minimise post workout hypos, it's good practice to have a small amount of carbs without insulin, or a reduced amount of insulin with the meal following your exercise.
The amount of carbs you'll need to eat post exercise to keep your BG up, or the reduction in insulin you'll need to implement with your meal, depends primarily on your genetic make up and the intensity of the exercise.