When Justin is reading the rules about what to do when the world ends, he reads that every wizard can bring ONE non-wizard. So he brings Zeke and Alex brings Harper. Max says he would bring his starfish. He could've brought Jerry or Theresa. But NOT both. And he stated he chose the starfish. So TECHNICALLY, it seems that both parents would've had to have been left behind.
The only way to explain the parents being allowed in would be if their father Jerry still counts as a former full wizard despite giving up his powers (or he may also be allowed in as the non-powered but official wizardry teacher for his children) and was thus permitted by the rules in the book to take Theresa with him as a (former) wizard. Apparently, once a wizard, always a wizard.
This is the second time that the Russo kids have put on Captain Jim Bob Sherwood uniforms, the first time was "Journey to the Center of Mason".