The group is correct re: switching the J-Arm over, however I would note that the device/J-Arm is not "supposed" to go over any given eye, dominant or non-dominant.
"Conventional wisdom" for many years was to place the monocular over the non-dominant eye mostly based on the theoretical rationale that your dominant eye could see "better," and therefore would give you more information if unaided, and also in case you needed to transition to your day optic while the NOD was still deployed, and aiming using the Bindom Aiming Concept.
While there are still plenty of folks who subscribe to and recommend this method, we (TNVC) and other experienced users have begun moving away from this for a number of reasons:
First the increasing prevalence of passive aiming--using your primary optics on an NV compatible setting and sighting through head-mounted NV. This is especially useful for pistols with red dots on them.
Second is that the theory-basis of running the monocular on your non-dominant eye has more or less been shown to not really hold out in practice--your better eye is your better eye is your better eye, and if you have a strong eye dominance that you've been using your whole life, putting the monocular over your dominant eye is more "natural" to both your eyes and your brain, while your non-dominant eye is "used" to giving supplementary information (binocular cues, peripheral vision, etc.).
The third reason, related to the second, is that especially in cases of strong eye dominance, placing the NVD over the dominant eye both produces less eye-strain for the user, as well as reduced mental fatigue (you may not realize it, but your brain is working overtime to process the more unusual information flow from opposite eyes), which can unconsciously lead to increased overall fatigue while using NVDs--ultimately. Ultimately, while you may not be conscious of it, running your NVD over your non-dominant eye means that you and your brain have to "re-learn" how to see, which then requires more training before it feels "natural."
Obviously a lot of guys (myself included) learned it the "non-dominant" way and used them like that for many years, to the extent that many guys are so used to it, they simply prefer it that way now--the point is not that there is a right or wrong way per se.
Try both and see which you prefer and which way is easier--and there's value as well in training both ways, so that you're used to using either eye aided. But don't contort yourself into using it one particular way because you've been told that's "the right way" to do it.
~Augee