Cabba was getting destroyed by Vegeta and he had no reason to believe that he wouldn't go and kill his whole family and destroy his planet, that's about as good a reason as any to turn into a Super Saiyan.
I swear to god if I see one more person completely ignoring what actually happened in the scene where Caulifla turned Super Saiyan I'm going to smash my face through a wall. Cabba explained that focusing your energy into your back and creating a tingling feeling is how people who already have Super Saiyan turn the transformation on, Caulifla tells him to teach her that instead and Cabba says he can't, it's something you need to feel first. Caulifla turning Super Saiyan in that scene is supposed to show how much of a prodigy she is, not how easy Super Saiyan is to unlock, and Cabba is surprised by it as well. The scene is so god damn straight forward, it LITERALLY spells everything out and yet people keep ignoring the actual dialogue because "HUR BACK TINGLES".