Emition baking

So I set some colors on a model to emit.

After that, on a separate texture, I baked the the whole model and set the bake mode to ‘Emition’.

Then, I aplyed the texture to the model I want to aply the emit texture. Set the coords to UV and the Influence to color(1) and to Emit(1). Problem is my whole model becomes very bright. Are there any known methods to bake emit materials onto a texture and then to aply it to a mesh?

Thank you.