When I attach my servo to a pwm pin. Does the arduino automatically tell the servo to go into the neutral position? or do we have to tell the servo to move there by coding it?
Servo will have 3 wires - +V, Gnd and a signal. The signal needs to be pulsed to move the servo, with specific timing. There is a Servo library that does this work for you as part of the Arduino IDE install, and there is information in the Playground on how servos work.
Short answer, yes, it sends the servo to the centered position.
You might want to check the two links in my signature for more information on using servos with Arduino in practical situations.
Duane B