I;m not sure what the exact solution is, but I can point you in the right direction.
ACF saves the image data as the attachment ID. This means the URL is generated dynamically when you use the get_field function.
ACF image field uses the wp_get_attachment_image_src function to load the image url data.
perhaps there is some documentation with the Domain mapping plugin which talks about using image functions like these?
Hope that helps
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