noren saidI should not have been jogging uphill on a treadmill.
Does this activity especially tighten the psoas and piriformis muscles?
Yes. You use your psoas to help raise your leg in conjunction with the quads (one of the many things you do with your psoas). So when you're walking up a stair case, theoretically, you should use your psoas more than anything else.
The reason people have psoas and piriformis problems is that they don't use them correctly. Most people compensate with the powerhouse muscles, i.e. the quads, hamstrings, and glutes. When this occurs, your other muscles don't work out and develop to their potential, making them vulnerable. So when you do finally exert them, they don't have the ability to perform, becoming tight.
You must, must, must release these muscles. I know stretching isn't really talked about in the gym world, but your psoas is not the same as your bicep. Those two muscles are some of your most important and constantly used parts of your body and they do not function in the same light.
You can't effectively build strength in either of them if they are too tight to perform. Release them, let them rest, and slowly perform isolating exercises. Remember if either of those muscles is out of alignment, it throws off your lower back and knees, which throws off your neck and shoulders and feet, which throws off everything else. Many aches throughout the body are actually caused my imbalances in these two specific muscles.