I feel there might be a little confusion on DPI here, as they are useful with printed media (dots per inch) but futile when taking into account digital media: If you are exporting an animated png sequence, I assume you're not going to print it. Standard screen dpi is 72, and animation atlases/sequences are made to be seen on a screen and not printed, but it really doesn't matter, as what really counts is the pixel size of your image.
You can find a nice and detailed explanation here:
VIDEO
If it's really important for you to have 300 DPI in the exports, you can do like the guy in the video I linked above at around 4:14 and re-save the exported sequence, you can also set a photoshop action and therefore batch your files to set the DPI at 300, but this is not going to change in any way the substance of the exported pngs, so don't worry (:
In general, just remember that Spine is already using an optimized compression algorithm to get the best images on screen with the smallest possible file size, and the same can't be guaranteed if you re-save images with photoshop.