Well, it's not so much the turning ability as the E retention abilities that can hurt instead of help in a rolling scissors type of situation. That said, planes with good sustained turning abilities generally derive that ability from good E retention.
Basically, in most scissors type situations, the plane that can fly the slowest, wins. In a rolling scissors, it will be the plane that can continue the maneuver at the slowest speed and still be maneuverable that wins. Often, planes that burn E quickly like an FW or my Jug, can force an overshoot because they can slow down very quickly in the early stages of a scissors. This is when a plane with a good sustained turning ability can be at a disadvantage, for example a Spit IX, since it retains E so well it can't slow down as fast as an FW could. However, if the "better turning" plane can avoid an overshoot and is more maneuverable at low speed, it will easily win the scissors once both planes have slowed. Often it comes down to how sharp the faster attacker is, and if he see's what is coming and takes action. A Spit IX diving on my Jug when he sees me setting up an overshoot will either pull off and zoom away, or saddle up. If he decides to saddle up and is sharp enough to use lag pursuit, chop throttle, and slow down as much as possible, I'm in deep doo. If (and this is often the case) the attacker neglects to decrease closure in time through whatever means, I will likely be able to force an overshoot and hopefully get a snapshot!
And yes, up to a point, turn radius and rate are greatly affected by your speed. The greater your speed, the larger your turn radius will be, and the higher your turn rate generally. You can use this to choose the type of fight that is best suited to your situation. If you are faster your rate is high but your radius will be larger than a similar plane flying slower, so you will want to chase his tail and use lag pursuit techniques to maintain position until you can get a shot. If you are slower, you will want to turn in a fashion that will get you front quarter shots twice every circle so you use your smaller turning radius to get a shot.
Naudet, your attackers were not flying to their plane's strengths. Just one Tempest driver could end your day by using lag pursuit methods and controlling closure. A tempest could saddle on you from a position of advantage, but he'd have to be willing to slow down to do it. Generally, slowing down is not something pilots like to do, so it often means you can sucker them into trying to follow your breaks and then overshooting. If the higher/faster Tempests either were willing to drop anchor and saddle on you, or simply BnZ and not follow your breaks, they could control the fight from relative safety.