If you have an integration template with mappings that are inherited by child integrations, you can adjust the mapping step on that integration template to propagate your new mapping to all the integrations using that template.
If you are doing so in order to update or sync a new field from your integrated system, the child integrations will not automatically reload to catch that a new field has been added. They currently need to be clicked into individually to reload the configuration and accept the new field mapping.
It would be helpful if updating or reloading on the Mapping step of a template integration automatically reloaded all child integrations that inherit that mapping step as well to make the transition more seamless.