No. Don't start up some small talk right then, unless they are clearly inviting it. Leave them alone, they did what you asked. After a couple of workouts, you know their name, they know your name, you are familiar to each other, then maybe you start asking what they do or getting to know more about them.

At least that's what I do. If someone I don't know at all asks me for a spot and then starts immediately hitting me with a bunch of questions/chitchat I'm suspicious. The last time this happened it turned out to be a guy who fancied himself a powerlifting coach and was looking for new clients.