Unfortunately every company is slightly different. I know HWA offers a 13-month warranty, which is nice, but whether septic in particular and to what extent is covered would be just a guess.
The "home warranty" is actually a type of insurance policy to cover primarily major systems in a home, including appliances. Some things are optional under the contract. Legally we refer to "home warranties" as residential service contracts, because the contract is to come out and fix or replace a broken item. This service usually requires a copayment or service call fee.
You can find a list of the currently licensed 30 RSC providers in Texas here: http://rowlett-realty.com/for-sale/home-warranty-information/
You'll have to check with each one whether they cover septic and to what degree, although I suspect most of them cover some aspects of septics.