Why is color replacement tool changing brightness?

This is a fairly common question. The answer has little to do with Photoshop, but everything to do with how we perceive light and color - and the energy distribution in the spectrum of visible light.

In short, yellow is an inherently very bright color at peak saturation. Purple is inherently very dark at peak saturation. The other colors fall along a gradient from light to dark.

This means that you cannot just "change a color". In doing that, you also have to remap the entire contrast range and contrast curve. The whole distribution of light and dark tones change.

The color replacement tool is a very coarse tool that has no idea of any of this. It just shifts the hue. That might work for very subtle shifts, but generally this is a pretty useless tool and few (if any) advanced users would ever touch it.

What you need to do is mask the required area, and then start working with a range of tools. This is not simple or easy.