The All in one migration plugin should automatically change the URL, it's automatic. If it fails, then any URL editing plugin will fail too.
I checked your site and it's not just those URLs in your screenshot, but the whole site remains served through www.digitalsolutionsbymd.com. The source codes remain the same if you'll check it in the browser.
There could be two possibilities,
- It's served from page cache since URL replacement only works with the database.
- Your site uses database caching, the URLs are replaced in the actual database, but the data from database cache is the one being pulled.
You could try cloning your site in a staging to a different host (just for testing) and so we could compare your setup.