Anderson, who ran as a Republican, took 61.81% of the vote against Renee Harrell, who had 38.19% of the vote.
Tijerina, who ran as a Democrat, took 54.85% of the vote against Greg Papst with 45.15% of the vote.
Williamson County Precinct 4 constable for the Democratic Party also had a contested race. Perry Travis beat out Hoby Smith with 58.2% of the vote. Smith received 41.8% of the vote.
Paul Leal ran unchallenged in the Republican primary for Precinct 4.
Constables serve in four-year terms as licensed peace officers who can issue traffic violations and serve warrants.
Election Day is Nov. 3.