Whilst Tracy was quite correct, I think the advice might not be applicable here.
Firstly, the question is if your blood sugar rises after exercise if you don't eat (much) afterwards. If it doesn't, then your high BG was caused by too much food or too little medication, depending on how you look at it. Exercise may continue to lower BG for several hours, but that doesn't seem to be case here.
Alternatively, it is possible for exercise to increase your BG (as described by daisy); in that case I cannot offer any advice. A quick google search, however, suggests that this is caused by insufficient insulin as during strenuous activity the liver converts glucagon to glucose, which will raise BG levels.
Edit to add: if you are saying that you had. BG of 12 mmol/l before exercising, and 5.9 afterwards then I don't think a hypo is very likely. I'd suggest that you testing every 30min, say, during and after exercising would be more helpful than us guessing based on two data points)