AI made a 3 tier with SMBC. I put the images on as soon as I iced it, then I put it in the refrigerator. It turned out great but the humidity was good and temperature was 70s. Taking out of refrigerator may be a issue of it's really hot out and high humidity.
It should stick and refrigerate just fine. If your cake is a different color (say chocolate cake with a white edible image) I would suggest adhering the edible image to a thin fondant / gumpaste / modeling chocolate sheet and then putting that on the cake. If the cake frosting color is dark it can bleed through the image. As far as taking it out of the fridge, I live in a high humidity area and I have never had an issue with one running, etc. Good luck!
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