Webpushify is based on the Push API. Push API is currently supported by the latest version of Chrome (desktop and Android), Firefox (desktop and Android), Opera (desktop and Android), Edge (Windows) and Samsung Internet.
Webpushify also implements the proprietary Apple Push Notification system to support Safari push notifications on desktop.
Notifications are delivered immediately even when the user is not surfing your website.
Chrome for Android, Edge and Safari deliver the notifications even when the browser is closed, while Firefox and Chrome on desktop need to be open (otherwise the notifications will be delivered upon opening the browser).
Note: Not every mobile device can receive web push notifications. Apple mobile devices (iOS) do not currently support mobile web push notifications. So, users using Chrome, Firefox, Opera, Safari and Edge on an iPhone or iPad cannot receive web push notifications.
Check browser support at: Can I use Push API?