Is there an iPhone app that will pop a message on another device? Is there an iPhone app that will let me pop up a message on another device (iPad / iPhone / iPod)?

For example I would have the app running on both devices and from my iPhone type "come upstairs" and it would pop up a message on the receiving device that shows "come upstairs"
Try Pushbullet for iOS, which is an app designed to let you instantly send messages, files, and links from one device of yours to another.

Pushbullet will let you sign in with one account on all of your iOS, Android, Windows, and macOS devices, and will let you write a message on one device and have it pop up as a notification on any or all of your other devices.