You asked about,
the view that the outer world is a reflection of one's own life state, not the other way around
I'm not sure that that is a conventional/orthodox view from the Pali canon.
I mean, maybe there are views that are like that ... but maybe not exactly like that, or nothing phrased exactly like that?
If someone weren't familiar with Buddhism then their first/naive interpretation of that phrase might be, "if 'the outer world is a reflection of one's own life state', does that mean so one's own life state is true and real contrasted with the outer world being less true or unreal (i.e. merely a reflection or illusion)?"
But I think that (saying that the outer world is unreal) might be (or might be, if it's misunderstood or taken to a naughty extreme) a wrong view:
And what is wrong view? 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no contemplatives or brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is wrong view.
According to western philosophy/language there's a view called Solipsism.
Moving on from there, some people who know very little about Buddhism might think that "Buddhism teaches that the outside world is an illusion".
I wondered where that belief might come from and found Maya (illusion).
If "Maya" is more Indian or Vedic than Buddhist, the more-Buddhist counterparts to that might be Saṃsāra (which is Sankrit and Pali), or perhaps Vipallasa (distortions of the mind).
I think that (Vipallasa) is a more standard view in the Pali canon: it's a view/philosophy that we mis-see, that we mis-understand the (whole, outside and inside) world.
I'm not sure about phenomenology in Pali, which I think is a subject of the Abhidhamma. So far as I know, the Pali canon doesn't say that the "outer world" is more or less than some counterpart "inner world". If you read about Ayatana it says that there are "external" and "internal" sense objects, maybe without saying that one is a reflection of the other.
On the other hand, "Rupa" (which I understand as meaning "forms" or "external objects") shows up among the 5 aggregates and the 12 nidanas ... in context maybe we should understand as saying that Rupa has some existence (though not "self-existence") but it's important because of its effect on our consciousness.
While I'm mentioning "rupa" let me also mention "dhamma", since other answers here talk about it ... it's a word with many meanings, I think one of those meanings is that it means "idea" ... I think the Sabba Sutta implies that dhammas are perceived by the mind, in a way that's similar to (no more and no less important than) the way in which forms are perceived by the eye, etc.
In a comment you mentioned the Vimalakirti Sutra: which I haven't read.Wikipedia says,
The sutra teaches, among other subjects, the meaning of nondualism.
I think that "non-duality" as a teaching will be found more in scriptures that are later than the Pali canon, so maybe there isn't exactly a Pali word for that philosophy.
If there is such a word though then it might be advaya ... Dvaya means "two-fold" or "dual"; so advaya means "not two-fold", "non-dual", or "single".
Maybe the Vimalakirti Sutra de-emphasizes the "outside world" by talking about "emptiness" ... the Pali word for that is suññatā.