Generally no, most campgrounds do not have purpose built tornado shelters. However; most do have facilities that can be used as shelters during potential storms such as camp stores, laundry buildings, bath houses, etc. I’ve lived in tornado regions all of my life. We have never made a campground decision that involved any consideration for tornados. It’s just a non-issue, YOMV.
Do you also consider you may be struck by lightning, a plane could fall from the sky, the camper next to you may explode, and thousands more catastrophes that could befall you?