If you have Signal on an iPhone what you want to do is deactivate previews in your notifications. This essentially means you can still get notifications but you can't read the text inside the notification, you need to open Signal to read the message.
This setting is good advice for ALL NOTIFICATIONS. Without it people can read messages on your screen. And if you don't set Show Previews to “Never”, these messages apparently are stored in a freakin' database on the phone.
