They were trained to perform their job of silencing high priority people. They had a big complex devoted to training their clan members in Ise, Japan.
The "hitmen" would be the rebels/ronin in the countryside, basically if you paid them enough money they would do their job. But sadly peasants only can pay so much, and rebels/ronin had a reputation of being less than faithful to their word. At least that's how it was during the Tokugawa Shogunite.