I've lived in Texas all life as well, and I've seen threatening weather, but no twisters hitting the ground. In reality, the biggest hazard I face day to day are drivers on the road.
I'd make sure you have a functioning A/C and electricity (generator or electrical campsite), as well as a good supply of cool drinks. Generally after this time in May, the weather gets hot and stays hot until September or October.
I remember when Lake Travis used to get partially drained to kill the hydrilla... well due to the long drought and the sterile (I hope) carp, that plant is long gone. I just hope the lake fills up because all the people moving to Austin are sure doing their part in trying to drain it.