Re: beginners question?
"then does the barrel lift up before the bullet even exits the barrel."
In a word.... Yes, but it needs qualification.
The rifle reacts to the bullet going downrange. The direction of barrel deflection/movement is due to the forces applied by the shooter or restraining device.
If you shoot right handed in the off-hand position and do not "lean into" the rifle but "go with the recoil" the muzzle will probably move up and to the right. This is because the forces acting on your body are directed toward the right shoulder causing some twisting and it also cause your body to "fall" (move) toward the rear.
If you're shooting from the prone position with the toe of the butt resting against your shoulder you will probably have some muzzle rise (moreso than if the heal of the butt is resting against your shoulder). You will probably not see any muzzle movement to the right if your prone position is good and the rifle recoils straight in line with the center of mass of your body.
As long as you are consistent in your position and reaction to the recoil your shots will be on target as the effect of the recoil is predictable and constant. Changing/inconsistent shooting position(s), figiting, flinching, "forcing the shot" all effect the difference between Point Of Aim and Point Of Impact.
Consider the effect of someone pushing against your body and the reaction it causes. Stand face-to-face with someone, relax (no slugging), push against their shoulder and see (closely observe) how their body moves/reacts. Imagine a rifle in their hands and the movement this reaction would cause. Try several different position (call it your "Carbine Sutra") and observer the difference in their reaction and movement... the less movement on their part means less chance for recoil induced projectile deflection(s)