Leo First, let me confirm your question. Are you hoping that the colors of each part image included in the texture atlas page exported based on slot colors will change? If so, Spine does not have a feature to change the color of the image itself. Only at runtime, the colors of attachments under each slot are changed based on the contents described in the skeleton data file.
However, if the issue is that the slot color does not change at runtime, this is not an export setting issue. It is possible that the runtime you are using does not support tint, or that the shader you are using is incorrect. Could you please check if the slot color is the expected color at runtime?