You need to acquire scandal points to be able to fire the trainers! I know that sounds strange, and I don't quite understand how it works myself, but after a 2-point scandal I was able to fire one trainer, which brought me back to 0 points.
But there is no probationary period and if they're useless, we're stuck.
By "useless", I mean when I hired a couple of basic trainers and tried to make them train my basic idols (beginning of the game), it was impossible: "max level 1". But it wasn't told before I hired them and they could do nothing except research.
If I wanted to improve the dance/singing of my idols, I had to recruit better trainers, but I had no money to build new rooms... and was stuck with 2 useless trainers draining my cash.
With a probationary period (or more info before I hired them), I wouldn't have had that problem.