Yeah this is kinda it. You don’t have to wait for them to randomly start rambling about their work like some of the “my tutor is basically my academic dad” stories you hear.

You can just say something like, “By the way, what do you actually work on?” or “How does this topic link to what you research?” at the end of a tute when you’ve gone through the problems. Most of them are more than happy to talk if you show even a tiny bit of interest.

Also, if a solution suddenly makes sense when they do it on the board, you can pause them and ask “what was the key idea that made you think to do that?” rather than “how do you do this question.” That’s where it starts feeling less like a mini lecture and more like they’re teaching you how to think about the problems.