You must obviously select the project that you want to publish.
You must click on the small arrow right next to the "Publish" button.
You must click on the "Publish to Multiple Companies" option.
On the smart panel that will appear you must select the companies that you want to publish the project(s). Only one company is also a possibility.
Check the check box indicating "Publish with Cleanup", this will make sure to reapply all item present in the customization project replacing the already present one with their newer version.