"Could you elaborate on that?"

When exactly do you use this phrase?
I feel like it's a bit too much to use this for a young person, even in a formal situation...

See a translation

You use it when you want further details about a subject.

And it all depends on whom you are addressing, if they are well educated or not, irrespective of your age and theirs.

Let’s say you are at a party, and you meet Neil deGrasse Tyson (an astrophysicist), you could talk to him about his hypothesis and say something like :
“I am fascinated by your hypothesis on X, but never could grasp Y part of it, would you be so kind and quickly elaborate on that? I’d love to hear it!”.
Of course in a “serious” formal setting (like a serious business meeting) with well educated people, it is perfectly fine.

You use the language that fits the addressees. It is different than Japanese. In English it is sophisticated vs unsophisticated language. In Japanese it is formal/polite vs casual.
In English it is called “using big words”. In Japanese it is “using formal form”.

President Trump in his rallies does not use sophisticated language, even though it is a “formal” setting.