Mine weren't for PhD interviews - I think that's quite strange you have been asked to do that! I've never heard of it for PhD interviews before, generally other than a basic interview people might be asked to do a presentation and that's about it.
For non-academic jobs, I have done tests before the interview shortlisting process and they have said what they are going to be on (maths, English etc). I have an upcoming interview soon where all I have been told is that there will be a test... so that should be interesting! For other non-academic interviews I have been asked to a prepare a presentation on a specified topic, using examples from my own experience, or been on assessment days where they say there will be a variety of tasks to complete but they don't say what they are. These tasks ranged from completing things as a group to trying to sell something to responding in writing to a customer complaint to multiple choice questions about different scenarios.