Hmmm, that *shouldn’t* be the case at all. Can you point me to a URL or something? This plugin’s running on a number of sites at my work (it was developed in that context), like 20 sites, and none of them have this type of behavior. Also, do you have any other plugins modifying images in anyway? They could be conflicting. Try going through plugins and deactivating them to see if any are causing an issue.
Make sure your custom theme is either using the_content(); filter. If you’re adding ACF Content it should work out of the box with the acf_the_content(); filter that’s applied via the ACF plugin.
As I mentioned above, if you’re developing the theme and need to explicitly use a function to call the credit you can test some of these functions: https://dongaines.com/acf-media-credit/#functions
Also, note that the very first image on this page (https://dongaines.com/acf-media-credit/, the one on the left, not the big background image) doesn’t have a caption and is showing a credit.
In addition, are you running your own version of ACF or relying on the plugin version? If so, what version of ACF are you running and have you updated WordPress core to the latest (4.7) version? I’ve just upgraded my site to 4.7 and see no issues.