If you’ve changed the domain name for the site, you’ll need to make sure you run a search/replace on the content to turn local URLs starting with “//olddomain.com/” to “//newdomain.com/” so that WP Offload Media recognizes the local URLs belong to the site and rewrites them to the bucket/CDN URL.
There’s a guide to changing the site’s domain.
We’d obviously recommend using either WP Migrate or Better Search Replace for that search/replace.
You shouldn’t need to do anything to continue offloading to the bucket, unless you removed WP Offload Media’s settings for some reason.
-IJ