Hmmmm so you are absolutely positive that there is no soreness issues? Issues with transitions and smaller circles in canter certainly indicated some soreness through the back. In trot it won't show up so much because he can keep his topline tight and 'fake it', but in canter his topline has to stretch and contract, and when you add a tight circle or transition into that, its understandable he'd get cranky if there was some soreness or even just tightness somewhere.
If it is not a pain/discomfort issue, the next thing I would look at is whether you are pulling him around the circle rather than pushing. It's easy to try and haul a horse around on a 10/15m circle, but you'll just land them on their inside shoulder.
Try thinking about riding a working pirouette feel when you come onto the 15m circle. Having that feel in your mind will help you to sit deeper and ride the hind legs on the circle rather than the shoulders. You can also try riding the circle more as an octogon shape, so straight sides with lots of little turns, again thinking pirouette in those turns. The more over the hinds he is, the better the circle will be. You want him in rear wheel drive, the front legs are only there to hold him up.
As for transitions, again if he's not sore, I would be riding MILLIONS of transitions every ride. Eventually, you want to aim to be able to ride only 1 or 2 canter strides at a time - THAT is having control over the hind legs in canter ;)
Just throw them in here there and everywhere, when I'm riding I try not to ride more than 12 strides at a time, at the same tempo of pace, I'm always changing things, adjusting, asking the horse a little deeper or a little higher, asking the hind legs a little quicker, maybe a little counter flexion, then some correct flexion... just shaking it up through every transition so you're not riding them dead straight every time.