I removed the background from my image using Photoshop and saved as a .psd file. (I outlined the image, and applied the mask so that it is a flattened photoshop file with a transparent background). I placed the images in InDesign and gave the whole canvas a blue background. When I print the collage all of the images have a visible background color cast within each image frame instead of being transparent. The same thing happened in Illustrator. I'm not sure if this a Photoshop or an InDesign issue but probably could be saving the images differently?
Can you share the file(s) in a Dropbox folder?