I would like to see how this would translate into other types. What are the "focuses" of the other functions?
Basically, the concept is that the aux function supports the aims of the dom function. Extroverts seek to affect the external & so their aux function can seem to have "extroverted purposes", if that makes sense. Introverts' aux function likewise takes on introverted purposes, such as to enrich their inner world of judgments or perceptions. This is why the aux function is often referred to as having a "creative" role, but that creativity is aimed at the dom function's focus.
These ideas are ones I've taken from various authors & MBTI experts who detail "roles" of functions for each type. My understanding of it is something like this:
In the case of JiPe & PeJi types....
JiPe types focus on perfecting a concept (which amounts to a judgment/conclusion) & use their perceptions to aid that. EXAMPLE: This means that INTPs use their Ne to find connections between external concepts & their internal framework, and they do this to perfect their internal framework, to consider the far-fetched in case it's actually right. No wonder the stereotypical jobs for them are mad scientists and reclusive theorists

. They have far less focus than ENTPs on affecting other people & the external environment.
PeJi types focus on pursuing their ideas/perceptions in external reality, and they use their judgments to support those pursuits. This means that ENTPs seek to affect other people/the external world with their ideas & they use their Ti logic to convince others or to explain an idea; for example, they might want to make a seemingly far-fetched idea a logically accepted reality. And so the stereotypical jobs for them are lawyers & comedians

. Just as I see ExFPs as having a "Fe-flavor" in their demeanor, ENTPs seem to have a Te-flavor. You'd never, ever confuse them with a Te-dom, but it's in the way they seek to affect others with their logical reasoning, wanting it to be accepted in order to further some idea they are pursuing. ExFPs also seek to affect other people more via their feelings & emotions, sort of like Fe types do, but in a very different way.
In the case of PiJe & JePi types....(and since I am not Pi + Je, this is harder for me to explain)
PiJe types focus on pursuing internal perceptions & the ideas they lead to, & they use their judgments to sort of weed out the less important perceptions (in the way Ji perfects concepts or the JiPe type's line of reasoning, PiJe types sort of "perfect" their perceptions by narrowing them down). EXAMPLE: This means that an ISFJ's impressions, or their Si "storehouse", is very much influenced by what they have decided is valuable in relation to others. This is why they are associated with being very intune with the needs of people important to them; they prefer to review the impressions they've formed regarding people & situations they have deemed most significant. This is partly why even though Si is highly idiosyncratic, forming very individual, subjective impressions of reality, they can seem very "homogenous" on the outside. They use external measures to gauge the significance/logic of their own impressions. When you get to know one well, then you realize what a massive individual bias there is in their perceptions & how this is really what is leading.
JePi types focus on perfecting external structures & use their internal perceptions to help build these. The ESFJ is focused on perfecting the harmony of the people & the environment and uses internal perceptions to recall what has & has not worked in the past, so that the external structure can further be refined. Again, the extrovert seeks to affect others. JePi people are very "production-oriented" in a sense. Where PiJe judgment weeds out lesser perceptions, JePi doesn't bother with pursuing ideas mentally that don't further developing their external structures. They're not building an internal storehouse the way ISFJs are; their perceptions are being sourced to build something that involves harmonious relationships or logical benefits in the real world.
They seem like subtle distinctions at times, but it has an impact on how personality appears. That's why the E/I difference goes beyond where you get your mental energy, but affects your whole mindset.