High Intensity exercise temporarily heightens Insulin sensitivity (Glycogen replenishment being one of the primary factors); this can differ significantly depending on how intense your session is.
I've been training HIT regularly for close to 10 years, initially I experienced frequent hypos, however through trial and error I established that reducing my basal (Lantus by 30 to 40 percent was the most effective course of action for my body) additionally my Novarapid requirements reduced by up to 50 percent post exercise.
So in short I would recommend reducing basal on training days (presumably you are also experiencing heightened insulin sensitivity the next day) and ensuring you have a snack pre bedtime; it's a case of testing, testing and re-testing to understand how your body is reacting to the exercise.
Can be a frustrating 'exercise', but once you establish a regime/routine, you can enjoy and reap the benefits of High Intensity exercise without nasty hypos
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Exercise = Endorphons > Euphoria (and all the associated health benefits and weight management)