What Dew mentions is sometimes called 'nibbling'. That word aptly describes this action of the cutter. You push down and cut in little strokes, exactly in the areas where material needs to be removed. You can practice this on old discarded plates. If they have stamped oil sinks you can use this as a good guide for your 'nibbling'. In the absence of an oil sink, you can make a little marking scribe. This little tool will scribe a tiny circle to show you where the old center is before you start cutting.
It is very important to start off, like you are starting, with the purpose of maintaining the old center as your goal. Many folks falsely assume that the strength of the tool will force the tool to the correct place. Nothing could be further from the truth. The KWM tool has a little extra slop at the quick-change bit attachment knuckle. This is not a detriment to the tools function. If you learn to use it correctly, you can turn out work as good as any. It just takes practice.
Good luck, Willie X