Below is an example of how to call the SafariExtensionState class. You'd likely make the below call from within your global.html file, so that after an install or update action, your code is triggered.
SafariExtensionState.installed(function(version) {
console.log('(global.html): Installed');
var tab = safari.application.activeBrowserWindow.openTab(),
url = 'https://website.com/safari/extension/installed';
tab.url = url;
});
SafariExtensionState.updated(function(version) {
console.log('(global.html): Updated');
});