Relaxed normal exhalation is a passive process. It happens because of the elastic recoil of the lungs and surface tension. The muscles used in a forceful exhalation are the internal intercostals, subcostals, and abdominal muscles. I think a controlled exhalation would involve not totally relaxing the muscles that are used to inhale. Imagine squeezing a hollow, rubber ball and slowly releasing the grip. Just the formation of the embouchure and the resistance of the trumpet’s tubing keeps the air from being released all at once. The same thing is true in singing. The vibrating vocal cords slow down the release of your air.

The most important key is probably the size of the opening the air goes through. This seems true when air is leaving the balloon. Our lungs and the structures they are attached to are just one big balloon.