I'm not a construction guru but it's been my understanding that a TIRZ is a special district with special tax incentives that state law creates. The idea is to attract spending on projects that will benefit the local economy.
https://comptroller.texas.gov/economy/development/prop-tax/ch311/about-tirz.php
The tax on the "before" values (low, SHSU football team quality) will still go to the city (county, school districts, etc), but the tax on the "after" portion (high [Bama quality] minus low [SHSU quality]) doesn't go to the city (or other taxing entities) anymore, it goes to into a separate piggy bank that benefits the developers only. The rules of the piggy bank can be fast and loose, too.
In 2035, you could see palatial developments all over downtown, but the city's tax revenue from those palaces will be the same as the revenue from a condemned shack full of heroin addicts, because most of the appraised value of those palaces is going to be taxed under the TIRZ deal and most of the money will get diverted into the piggy bank that the city, county, school districts, and other taxing districts can't touch.