[g_p]

To add a data point, my advisor told me to do the same. In fact, I actually spoke to one of his then-RAs who was leaving to go to the other side of the world (by sheer coincidence).

That discussion confirmed I was making the right decision, and I was able to gauge as well from the "warnings" I received that I was going down the right route. So I would definitely echo the above, and advise you speak to at least one of their previous students. If none are still around, that might be a red flag (or they might all be getting snapped up right away into jobs, but they will make the time to discuss with you, if they felt their advisor helped them!)

I would personally find it surprising if someone who wanted me to advise them didn't seek views from those I had advised previously.