A vsix package shouldn't rely on the registry for its settings, there is a specific API to access the Visual Studio settings systems. A normal vsix package cannot call or start anything after deployment. You can let the package itself setup defaults the first time it is started.
If you really need more advanced things during your setup, you can create a .msi
instead of a vsix. You'll need to extract your vsix and include its contents in your Windows Installer package. Or you can use WixToolset to create a MSI installer and use the <VsixInstaller>
element to register the Visual Studio Package, you can put the other logic in the Wix installer project.