If the package does not have a parent dependency on itself, then you do not need to configure the publisher in the global zone, and you should not install the package in the global zone. Updating the package in the global zone will not update the package in the non-global zone. In this case, updating the package in the global zone can cause unexpected results when testing the older non-global zone package.
The simplest solution in this situation is to make the publisher available to the non-global zone, and install and update the package from within the non-global zone.
If the zone cannot access the publisher's repositories, configuring the publisher in the global zone enables the zones-proxy-client and system-repository services to proxy access to the publisher for the non-global zone. Then install and update the package in the non-global zone.