In this scene, the people you mention meet out on the street. Tybalt starts insulting Romeo and his friends. He calls Romeo a villain. At that, Tybalt and Mercutio start arguing.
Benvolio tries to calm things down. He asks them to at least get out of the street. He says that people are watching them (remember that the Prince has said that they have to stop fighting).
Romeo doesn't want to fight Tybalt because Tybalt is now his relative in a sense, since he is Juliet's cousin and Juliet and Romeo are now married to each other.