How can I turn off automatic full screen animations in iMessage / iOS 10?
To stop screen effects on your device navigate to Settings -> General -> Accessibility -> Reduce Motion -> ON.
When Reduce Motion is set to ON, no screen effects will be visible on your device and screen effects cannot be sent in the Messages app. However, messages that contain key phrases still automatically invoke screen effects when sent to other devices. For example, sending the words "Happy Birthday" will show balloons in the background on the recipient device, unless that user also has Reduce Motion turned ON.
iOS 10 brings a long list of screen effects, stickers and animations to the Messages app. Anyone with an iOS device running iOS 10 can send and receive iMessages with screen effects, including lasers, fireworks, and balloons.