Hiya,
Have you been drinking enough during exercise? I find if I get dehydrated (through sweat etc) I sometimes get ketones even though my blood sugars remain normal.
What I have found over the years is that if I am doing intense exercise such as HIIT, Metafit or interval circuits my sugars jump up fairly fast and take a while to drop back down. When I do things that are more steady state like jogging or cycling etc my sugars tend to remain stable and just react more to the food I've eaten prior to the exercise. When I am weightlifting my sugar levels change depending on how heavy the weights are and how quickly I complete the session (If I do things like supersets/drop sets/high reps or just steady controlled sets).
I've found keeping a close eye on my blood sugars during and after the exercise plus making sure I drink enough fluids really helps, I've also tried to make sure whatever I eat beforehand is really well balanced so that it doesn't cause a big spike but gives me enough energy to perform!
Sorry if none of this makes sense, tried to explain as best as I could! Hope you manage to get it figured out, I know how annoying and disheartening it is but try to stay as positive as you can, you'll find a way to make it work for you eventually it's just trial and error unfortunately!!!
xx