You did the right thing by grabbing the mattress and running for a safe place. I'm glad to know you are safe!
It's hard to leave the pets behind, but you would have been severely injured if you had gone out looking for them. Lee intelligent people would have been outdoors or (worse) running for the camera.
Any time there is a Severe Thunderstorm Warning, there is the possibility that there will be a tornado. Radar will not always pick up a tornado touchdown, so meteorologists depend on trained spotters to make reports about what is happening on the ground. Luckily, you were in an area where you could be warned ahead of time; someone must have spotted the tornado and called it in to the NWS and emergency personnel.
Few people realize how dangerous severe thunderstorms can actually be and how quickly a tornado can form. No less dangerous is the flash flooding, large hail and things like downbursts that these storms can produce.
--- trained SkyWarn spotter (contact your local National Weather Service branch office if you would like to join us; training is free and is held several times a year)