The exported .json file itself does not contain information about whether the images were exported with the Premultiply Alpha option checked. However, the atlas file associated with the images can contain this information. Specifically, if the atlas is in the newer format, it will have a pma: true field indicating that the images were exported with premultiplied alpha.
For example, in the context of the command line tool, it is mentioned that:
"since 4.1.26-beta of your atlas is in the newer atlas format, it will have pma: true in the atlas file and the unpacker will perform un-PMA."
Therefore, you should check the atlas file for the pma: true field to determine if premultiplied alpha was used.