I am afraid there is no solution. While this is not related with the plugin, since AJAX request should fetch also the plugin code and not only its HTML. The way this is handled will work only with static content. Please consult your theme provider on how to load plugin scripts after the ajax call
Can you tell me which scripts or code of your plugin need to load after ajax call ? do you have provide some custom js code to trigger reload your scripts ? if your plugin does not support load your player in ajax then no way to make your plugin work the other themes of plugins which use ajax to load content without edit your plugin code
You are a developer and I think you know this problem
This is the script your-domain.com/wp-content/plugins/audioigniter/player/build/app.js?ver=1.7.2
Loading content via Ajax for static content is bad practice, unless you have a single page app. In any case this requires additional coding which is not supported by AudioIgniter I am afraid. I believe any related dynamic plugin will never work unless you load its scripts after the ajax requests that fetches the HTML.
I’m not sure about “Loading content via Ajax for static content is bad practice” but I think 99% filter post plugins of WordPress uses ajax to load content and if you do not support ajax that is a big minus point for your plugin, because almost or theme still use ajax to load data