The rate of pressurization/depress is generally computer controlled, but can be manually controlled by the crew. If you ran into one that felt like it was changing in steps instead of a smooth rate- it may have be in manual mode at that time.

The air for conditioning/pressure is supplied at a mostly consistent pressure from the engines (~54psi on a CRJ-900; depending on bleed air requirements), and the cabin pressure is regulated by an outflow valve (generally in the rear pressure bulkhead).