First peak at Crystal Tower?

[yukikaze_yanagi]

I believe that cutscene is exclusive to a specific city-state, isn't it?

I started with Ul'dah then joined the Maelstrom and haven't ever seen that CS. Watched it on YouTube though.

And you're wrong, because i don't speaking of any cutscene.
If you did MNK quest, go speak with professor Erik, then choose Class is in session -> Silvertear Falls.
At the end of speeching, he found a huge tower below the lake. Since he's emanating huge aetherial energy and common stone can't do it, he believe it's made of crystal.