In some cases, they ran in districts that were already heavily Republican, often due to gerrymandering. They won because any Republican would have won.
If other Republicans ran in the primaries, they won the primary by exciting the primary voting base. Far fewer people vote in primaries, and they tend to be engaged in hype, and MAGA is all hype based propaganda based on fear and anger. That excites Republican primary voters.
The few that defeated incumbent Republicans did so through the hate and fear angle, because it works. It is a successful fascist playbook, as shown throughout history.
So basically they mostly won for the same reason Trump won in 2016, fascist propaganda stoking fear. They promised to solve all the problems they made up about the groups they blamed.
The whole Ohio immigrants eating pets is just the same thing, dialed up to 11.