Quiet time is something a lot of preschool aged children have difficulty with - I would suggest trying to make quiet time a more 'enjoyable' time for him. Does he like music? Either a CD player on or something where he has his own headphones. Favorite books or stuffed animals and blankets.
Explain to him that it's quiet time, and that not only does he have to stay in his room, but he has to stay in his bed. He is definitely at an age where he'll try you and will get out of bed, and come out of his room a million times- but you have to be consistent in putting him back in bed every single time. If he cries or screams, let him. As long as he is hurting himself, you, or damaging anything, crying won't harm him.
It could take a few days, or it could take a month, but you have to be consistent

Hang in there!