Hi - so we've been having many issues with this plugin, especially with the latest updates to WP and not being able to upgrade because it breaks core. We've recently been in touch with Jetpack because we've had to code some custom plugins to allow Jetpack to work because of the Domain Mapping plugin. We sent them an example of what we had to do and this was their response (keep in mind that the plugin we had to create was necessary for Jetpack to even connect to a mapped domain by manually setting the REST API url)
So your plugin changes your REST API url when on the Jetpack plugin page. The problem is that Jetpack also calls that url from WordPress.com, and other plugins can also use that url, so it would need to be changed everywhere, not just with Jetpack.
At this point, we'd advise you to get in touch with WPMU dev, as this seems like something that should be fixed in the domain mapping plugin directly, as it affects any other plugins that want to use the REST API, not just Jetpack.
Are there any plans on updating the functionality of this plugin?