"PMR starts because your body is not producing enough cortisol."
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My understanding is cortisol levels are "normal" or "above normal" when PMR starts. However the body isn't producing enough cortisol under the circumstances that are present at the onset of PMR. Keep in mind that cortisol is the "stress hormone" and the production of cortisol needs to increase significantly during stressful times. While a person's cortisol level might be adequate for normal average circumstances, it is inadequate for more stressful situations. People say stress is the trigger for PMR.
https://academic.oup.com/rheumatology/article/39/6/624/1783929
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The body screams for "more cortisol." The way the body lets us know about a cortisol shortfall is how PMR feels. This might be a short term shortfall of cortisol and people are able to taper off Prednisone quickly.

The autoimmune part is different in my opinion. The way it was explained to me for "reactive arthritis" is that it is triggered by an infection. The infection I had at the start was severe so my need for cortisol increased significantly.

Whether it is an infection or some other trigger it is called an "antigen." An antigen can be almost anything. An antigen may be a substance from the environment, such as chemicals, bacteria, viruses, or pollen. An antigen may also form inside the body.

Regardless of the antigen it is something the immune system will attack. Many times these antigens are "chemically similar" to the body's own tissues. The immune system "misidentifies' our tissues and mistakes them for the antigen. Since our own tissues will always remain, the immune system will eventually develop a memory for attacking our own tissues. This sets the stage for "chronic inflammation" and an autoimmune disorder.

Initially I think the body uses both the endogenous cortisol from the adrenals and the synthetic exogenous form of cortisol that prednisone supplies. As inflammation subsides the need for cortisol subsides. Decreasing the cortisol level should be done by the mechanism called the HPA axis. However, we are told to take excess prednisone instead of allowing the HPA axis to reduce our cortisol level naturally.

The body tries to compensate for having too much exogenous synthetic cortisol by shutting down the endogenous cortisol from the adrenal glands. This sets the stage for adrenal insufficiency if we take prednisone too long.

All is well except for Prednisone side effects from too much Prednisone until we taper our prednisone dose lower. Somewhere in single digits of prednisone, we have a cortisol shortfall again. We take more Prednisone and the cycle continues until our adrenals resume cortisol production again. The adrenals won't resume cortisol production as long as we are taking more Prednisone than the body needs. However, if we don't take enough Prednisone, the body will scream for more.