The Png or Tiff has the original background? It you save the png with a transparent background where does the original background come from. Ping does not support layers and I would think that file format would not save pixels that are masked off with an Alpha channel. Saving that pixel data would increase file size. Tiff supports layers and Jpeg does not support transparence but the transparent background would be a solid color in a jpeg not the original background..
I find the PNG on Amazon drive do not display correctly on my PC using Amazon drive in my browser but they download to my PC fine,
Example from amazon drive
From my machine from downloading the above linked image on Amazon drive using Amazon interface
The displayed image using Amazon drive seems to be some jpeg they create not the png you saved on the cloud drive.
How they create it is unknown to me
Now I am having another issue with exported files. This time all the jpegs that I exported from the original tiff files show up as PNGs when opened in InDesign...
I do not use Indesign, Photoshop open jpeg files as a Background Layer in a Photoshop Document for jpeg file format does not support transparency. Photoshop opens a png file as a normal Photoshop layer for png file format supports transparency and may contain transparency. If your Indesign is opening a jpeg as a layers that contains transparency. I think you have an Indesign problem or the file format that you opened was formatted as a png not jpeg.