Actually no, it's the wind.
Even with the windows closed, most houses and commercial buildings have enough openings to vent the pressure difference in the time that it takes for a tornado to pass. The engineering team at Texas Tech's Institute for Disaster Research (Minor et al., 1977) point out that the pressure drop inside a tornado with 260 mph winds is only about 10%, or just 1.4 pounds per square inch. Most buildings can vent this difference through its normal openings in about three seconds. That is sufficient time even if the tornado is moving forward at a very rapid 60 mph. In the real world, the discussion is pointless. That violent a tornado would totally blow apart a house before the central low pressure ever arrived. Venting of air to relieve pressure would not be an issue.
BULLETIN - EAS ACTIVATION REQUESTED TORNADO WARNING NATIONAL WEATHER SERVICE MOBILE AL 351 PM CDT SUN AUG 28 2005 THE NATIONAL WEATHER SERVICE IN MOBILE HAS ISSUED A * TORNADO WARNING FOR... GEORGE COUNTY IN SOUTHEAST MISSISSIPPI MOBILE COUNTY IN SOUTHWEST ALABAMA * UNTIL 430 PM CDT * AT 348 PM CDT...NATIONAL WEATHER SERVICE DOPPLER RADAR INDICATED A SEVERE THUNDERSTORM CAPABLE OF PRODUCING A TORNADO NEAR KUSHLA... AND MOVING WEST AT 25 MPH. * THE TORNADO PRODUCING STORM IS EXPECTED TO BE NEAR... SEMMES AND LOTT AND COLEMAN DAIRY ROADS BY 400 PM CDT SNOW AND TANNER WILLIAMS ROADS BY 405 PM CDT BIG CREEK LAKE BY 410 PM CDT TANNER WILLIAMS AND BIG CREEK LAKE DAM BY 415 PM CDT