The shortcode only gets the image ID automatically if the image is attached to the post, so if NextGen is doing something funny and the image isn’t attached to a post as usual, or if you uploaded through NextGen first and then wrote your post you will need to use the image ID in the shortcode (https://www.kristarella.com/exifography/#shortcode).
I don’t know NextGen well, but last time I looked at it for someone I noticed that they have these template things with which you can modify the output of the plugin. They also have their own built in EXIF stuff to some extent, so you might want to check their documentation for how to display it.
In theory Exifography should work fine with NextGen, but I don’t know if it does any image manipulation to change the way images are processed and stored by WordPress. If it does that heavily then maybe the EXIF data is not stored in the WordPress database as usual.
