Spine assumes all PNGs it loads are sRGB. If you save a PNG for a different color space, the colors will be incorrect in Spine. Only sRGB images should be used with Spine, whether using the PhotoshopToSpine script or Spine's built-in Import PSD
.
All game toolkits I've ever seen load images using sRGB, so even if Spine respected the color profile specified inside the PNG files, the images still need to be sRGB to be used in a game toolkit.
If you use an ICC monitor profile you can enable Color Management
in Spine, so Spine renders colors correctly for your monitor. Note that is separate from your PNGs. You should still be saving PNGs for Spine using the sRGB color space, even if you use an ICC monitor profile.