So does this mean that what I'm experiencing at the dojo in terms of sempai ordering me around is not a 'normal', universal occurrence?
Not only not universal, but I believe going to the extent you describe it is the exception (for worst).
There are two totally seperate issues:
1 . In many Japanese Martial Arts students are expected to help and accept responsibility on them.The senior students are expected to accept more respnsibility to them and do more not less.
The teacher himself should set the example, and be the first to do most tasks. The students may
show their respect to the teacher (who might also be much older or even old) by doing things for him, and replacing him. Again, the more vetran students should be the first for that, and the newer students should learn from their example (even without any verbal instruction).
2. The Sempai / Kohai relationship, means that a junior is expected to respect his seniors, and follow their instructions. In the places I know of, almost all instructions would regard the practice itself.
I have been a relativly vetran practioner in my sensei's dojo for a few years. When I thought the dojo was dirty (after/before class), I started cleaning it myself without asking anyone (Senei was still taking care of the office issues). Most of my "Kohai" and in some cases my Sempai simply saw me and joined (unless they had something else to do, which they deemed more important). Same goes for me when another decided cleaning was neccessery. Often, someone came to replace me (we only have so many cleaning tools), in other cases, I replaced another. I only asked another to replace me if something more important came up in the middle (Sensei asking me to come, a call, ...).
The way you describe things sounds very problematic to me. If the issue is not your owm over-sensitivity and your description describes the actual situation, something is very strange there. I also do not get the situation in which one Sempai is giving all the instructions and Sensei is letting him.