There is a historic way to present your alert in other apps, which can date back to iOS 5 or even easier.
You can refer to those links.
Can you use CFUserNotification with IOS 5.1
Display CFUserNotificationDisplayAlert on iPhone Lock Screen
There is even a wiki page on iPhoneDevWiki, CFUserNotification.
(Update 1) Here is the official source code from Apple.
Recently, this guy who comes up with a possible way of using this old method to steal Apple ID.
Continue reading Bypass sandbox and present an alert in other apps