Emet Selch Incongruence?

Why did he built his Museum/Monument to Amarout in The First instead of the Source?

I have known the Sources is not equal to the "world before" and that eventually if their plan of rejoinings were to reach it's end even The Source itself would go through extreme changes (more than any calamity) to be made whole.

Yet considering a similar fate. And that anyway Reflections ARE rejoined to The Source.

Why built his "work" there?

Why also we find remains of Amarout and the Unsundered in The First instead of the Source? For someone so fixed on how Reflections are less in all ways, shapes and forms from the Unsundered how does it fit that he makes his "monument" in a "lesser Reflection"?

He didn't 'build' the fake Amaurot insomuch as simply layered it over the ruins of the real thing like a glamour (it's basically a giant magic spell - Y'shtola states that the place is basically "swimming in aether" that she can see it clear as day through her aethersight). But more to the point, he did it partially due to blind nostalgia. Emet is actually a sad, tired old man trapped in his memories of the past - his whole character arc was basically stuck in an extended debate between himself and his ideals of wanting to recreate ancient pre-Sundering Etheirys, and the present sundered world with it's new life. His character development is finally learning to let go of the past which is dead and gone, and embrace the future - symbolized by the WoL who happens to be the reincarnation of his old pre-Sundering friend...

So he surrounds himself with this idealized recreation of Amaurot at the height of it's civilization, as he was cursed to remember how things were (or how he prefered to remember how things were - ignoring the dark undercurrent that lay just beneath the surface and ultimately led to it's destruction). He's just exhausted from having to bare the burden of his people's legacy as one of the remaining Unsundered, and so the recreation of Amaurot acts as kind of a stress release, and also a reminder of what he's fighting for.

As for why the recreated Amaurot is on the First and not the Source, Y'shtola actually stated that due to the constant cycles of Calamities on the Source any remnants of Ancient Etheirys like Amaurot would have long been obliterated or buried completely under solid rock on the Source - so the First's remnants surviving was the logical choice for the recreation, especially as he was already there on the First to set the Shard up for the Eighth Rejoining.

In-universe, the reason there are remains on the First but not the Source is theorized by Y'shtola (and pretty plausibly) to be because the Source has had a bunch of Calamities to grind the ruins down to dust, while the First has only had to deal with whatever the Sundering was on an 'impact' level and then twelve thousand years of wear and tear. That still did a number of them, but imagine how those same ruins on the Tempest would've struggled to hold against the earthquake of the Fourth Calamity, the mass freeze-and-thaw of the Fifth, and possibly even the sheer force of the Seventh.

As for why Emet built Fake Amaurot down there? Well, yeah, as far as we know there's no functional reason why he couldn't have done that on the Source, he's a magic super-wizard with the limits of his power determined only by writer fiat. So instead we look to reasoning that's more about in-universe logic, and there's a couple possibilities: there's conflicting theories on if that was something he made for himself to wallow in, or for us to find; if it's the latter, it makes sense that he slapped it down there knowing he could bait us there pretty easily, but if it's the former it's just an arbitrary decision that happened to line up.

...and in both cases, we have to remember that this is a video game being written for an audience. In which case, we just have to remember that Fake Amaurot is ultimately a setting, in a video game expansion, that was set on the First: you couldn't do the ending of Shadowbringers if Emet had built Fake Amaurot anywhere else, therefore Fake Amaurot is built where it makes dramatic sense for it to be.