Yes. The TPIC requirement exists at almost every major US airline. It helps to prevent the crap we see in Europe with people buying hours on type in the hope of landing a job on an A320 or 737 right out of flight school. That being said, getting paid poverty wages (c. £14,500) in your first year at a US regional makes it feel like you're paying to fly anyway.
Southwest is a VERY senior airline, most pilots who join have well in excess of the 1,000 hours of turbine command time that is requested. It's nearly impossible to get in without at least one internal recommendation.