There's quite a lot of stuff in
Psychological Types that reasonable people can disagree about, but I don't think this is one of them. In talking about "judging observers" and "perceiving observers" in that quote from Chapter 10, Jung is talking about J-doms and P-doms. One reason we know this is that Jung made the exact same point in Chapter 4. In explaining why Jordan (an Ni-dom) viewed introverts as the "more impassioned" types and extraverts as the "less impassioned" types, Jung explained that it was because irrational types (P-doms) like Jordan — and note that Jordan was a Pi-dom, not a Pe-dom — tend to type people based on their unconscious sides. And Jung explained that, by contrast, rational types (J-doms) like himself tend to type people based on their conscious sides. As he put it: "Thus Jordan's formulations accord on the whole with reality, though not with the reality as it is understood by the rational types, but with the reality which for them is unconscious."
And in Chapter 10, after making the same distinction in that paragraph you quoted, Jung reiterated the fact that, as a
Ji-dom, his own tendency was to type people on the basis of their conscious sides. As he put it (in his summary of the "extraverted rational types"):
So, contrary to your interpretation, it seems clear to me that Jung thought that an irrational observer (N-dom) would tend to type a subject based on their unconscious side whether the observer was an Ne-dom or an Ni-dom (like Jordan) and that a rational observer (J-dom) would tend to type a subject based on their "conscious psychology" whether the observer was a Je-dom or a Ji-dom (like Jung).