This is true in our world where dreams are just products of your mind. In Thedas, dreams take place in the Fade, which is shaped by spirits and the memories of mortals. The dream you're in doesn't just disappear because you woke up. Think of the Fade section in Origins. Those were dreams crafted by Sloth and maintained by his minions, and they didn't vanish because you woke your companion up. As for spirits - Solas himself says that after his friend was killed, he returned to the place where she dwelt in the Fade. Meaning it didn't disappear either. So, no, I doubt Crossroads were maintained by the Evanuris and only fell apart because they were gone.
Agreed about Solas being often contradictory, though. I wouldn't say he's deluded or misremembering because, frankly, there's no evidence for that. I think it's more because he's always leaving things out or talking in doublespeak - Trespasser was a rare moment where he told us some stuff straight, but he still kept a lot under wraps. It's unspeakably frustrating.
Yeah but the Fade world keeps changing. It doesn't stay the same for long unless there is some ruling spirit/demon keeping it that way. So mages who go there might exist in a certain "world" but when they wake up that world will disappear. Non-mages might just float around various "worlds" of spirits, or they might have their own world that morphs around them based on their own spirit's memories and thoughts.
As for the Fade sections in Origins, those were domains of a ruling demon. The Sloth Demon controlled it all. It remained until Sloth was destroyed. Then everyone left and woke up. It would be safe to conclude that this "world" no longer exists. The people you help talk about the dreamers there and how you must defeat Sloth to free them. Same case with Connor's demon. She even tells you that you stand in her domain. Also, the minions did not maintain those worlds. Sloth did. You didn't wake your companions up. You just helped them get out of those nightmare "worlds", and those would not disappear immediately because the Sloth demon was controlling those worlds too, just like "Weisshaupt".
I didn't write that the Crossroads dimension was maintained by the evanuris. I wrote that the "worlds" or places within the Crossroads may have been maintained by them.
There is no hard evidence for it. At least, not that I know of, though I haven't really searched for any. But the legends at the temples say one thing and Solas says that's just one version. He thinks of himself in another way. My main reason to distrust what he's saying is because there is no evidence of what he's saying. All we know are what some shattered spirit in the shattered library said, and now what Solas claims happened. That isn't enough to go on, in my opinion. So I don't think there's hard evidence for Solas' claim either.