Do the media IDs get saved to the database?
Search wp_postmeta for the post ID and meta key. It should have a serialized value containing the post IDs of the images.
My guess here is that the values are saved but then not rendered properly when the post reloads. This is likely do to functions called when rendering the fields and selected images that may not be captured/filtered/altered by the other plugin that you are using.
These include wp_prepare_attachment_for_js() and get_compat_media_markup()
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