Occasionally, after picking a new culture their emblematic quarter does not show up on the list of possible constructions in my cities. Not sure if this is a bug or I'm missing something.

Yeah... I was wondering about that too.  I picked the Mauryans for my Classical Era culture, and I haven't seen a Stupa anywhere and it's not on the tech tree. 

Anyone else having this problem?

Same here, I didn't manage to build one stupa. I didn't find it in the tech tree, or elsewhere.