Reversal has three meanings. Yes, it can mean a reversal of roles, i.e., from defensive to offensive but there is also the reversal of direction and of turn. Turning a left turn into a right turn is a simple turn reversal. For instance, you're in a left turn into a bandit to force a flight path overshoot. When the overshoot happens you reverse to a right turn into him. This may, or may not, result in a role reversal. In a directional reversal you're actually characterizing the intent and nature of the turn and implies the quickest possible change of direction related to tactical needs. For instance, you extend and accelerate to gain some separation then reverse (also called pitchback) to bring your nose on to the nme. The most efficient way to do this is usually a high-G wingover to minimize your turn radius and regain lost E after the turn. The OP is specifically talking about a vertical reversal which is a reversal of direction done in the vertical (duhhh

) and a vertical reversal can also be a rudder reversal. While this can be related to a rope, that certainly isn't the only time it's used.
The best procedure for the vertical reversal varies according to the airplane and the specific tactical situation. The position of the target (i.e, offset) and distance are considerations. If the target is directly below you, turn radius becomes important and you want to minimize it so you can come straight down on him. If he's directly below you have to be slow (probably less than 100mph in most airplanes) then stuff in a bootfull of rudder to yaw the plane over. This is a rudder reversal. If the bandit is offset from you and you have the speed sometimes it's best to just drop the flaps and pull the nose over.
If you're going to do a rudder reversal you have to know your aircraft's torque characteristics. For instance, in an F4U you have lots of torque that makes it hard to go right so you should go left using left rudder. This gives you both rudder and torque working for you to bring the nose around. You can sometimes plan for this by offsetting a bit to the right and keeping your target a bit to the left as you go vertical so the left reversal works from a geometry standpoint. If you must go right then pull your throttle back to about 1/2 to 3/4 to reduce the torque effects then use the rudder. Most airplanes in AH will have a pronounced roll associated with the yaw. This is true also in RL but is a bit worse in AH because of combat trim which wants to pull your nose "up" at slow speeds. It's usually not a big deal and you can just let the airplane do it's thing but sometimes a bit of forward stick helps if the airplane tries to just flop over on it's back. Also, after the reversal, as the nose comes down most planes usually aren't polite enough to just point straight down right away and will wander around a bit, especially if you're really slow (these motions are called post-stall gyrations) so be prepared to use control inputs (usually forward stick and opposite rudder) to regain control and get the nose pointed where you want it.
The best way to learn what works best for a particular ride is in the offline mode or in the TA where you can practice it. Ask for tips for a specific plane (they're all different) and you'll find that there are usually several preferred pilot techniques. What works best for one pilot may not be best for another. Try out different speeds, yaw direction, throttle settings, and amount of control inputs required. Keep in mind the goal is to get the airplane to swap ends as quickly as possible and point it at something.
Also, Dawger's correct about the use of a vertical reversal in a multi-bandit environment. In RL going pure vertical and getting slow at the top is sometimes called "a bandit gathering turn" as all the bad guys will see you as a slow target and head your way so use it judiciously if you don't want to become a pincushion.