Motorcycles handle upward or downward turns the same. The difference is in putting rider weight on the handlebars. When going uphill, it's natural to sit back and be very light on the bars (as well as getting a better feedback on acceleration/deceleration), but not so downhill. When you put weight on the bars you have to steer harder to overcome it.
The way to avoid putting weight on the bars is by hugging the tank with the thighs and holding your body upright with your back, and leaving the bars for steering purposes only. Check that you're not locking your elbows by tucking/folding your arms in from time to time. That's also a reason to brake before the turn and let go in the turn itself. Braking will move weight forward to the steering head.
BTW, engine braking has all the effects of braking, but while you can let go of the brake lever, you usually carry engine braking with you through the turn, and should therefore get in the turn slow enough so you can accelerate to overcome it.
An exercise that will convince you it's possible to ride downhill without weighing on the bars: put the side stand down, sit on the bike in riding position, fold your arms on your chest, and have someone push your back forward. Hug the tank and resist the push with your back without using your hands.