It is only a screen issue when transparency is added to a spread as it is here happening. Use PSD, that is the best for InDesign or PDF, don't use PNG. TIFF is ok, but has worse screen preview.
Try changing the Transparency Blend Space to RGB.
Thanks for the quick reply.
Changing the transparency blend space to RGB did it!
For those who don't know where to find it, it's here:
Edit --> Transparency Blend Space --> Document RGB
Keep in mind, though, that if the destination is print the colors will eventually get converted to CMYK and there will no doubt be some clipping of out-of-gamut RGB colors, so the print will look more like the rendering you saw before. Still better, though, to do the blend in RGB before doing the conversion.