Issue with images with transparency

I have tried importing an images with a transparent background into InDesign (PNG, TIFF or PSD formats). The pages where the images are placed have a 15% opacity colored background (See screenshot below).

It appears fine onscreen or even after exporting as PDF. But when it's printed, it a "burnt" color appears on the images where the transparency should be (See screenshot below). I can't figure out why that's happening. Both the images and the InDesign file are CMYK. I even tried adding the exact colored backgrounds from InDesign to the images in Photoshop so eliminating the transparency, but then with this it's worse because I now see the color discrepency onscreen. Please help! Thank you.