Do not show iMessages on iPhone when using Messages on Macbook Is it possible to somehow temporarily disable iMessages on iPhone when using Messages app on Macbook, I don't like my iPhone to vibrate and wake up on the table all the time when someone sends me a message when I'm chatting through Messages app on Macbook?

I notices, that sometimes it vibrates for 1-2 messages and then it stops for the rest of conversation, but now it's showing almost every message on iPhone
The function of iMessage is to push your messages to all devices. To turn this off, go to Settings > Messages and disable iMessage. However, this is certainly not automatic, and may remove your cache of message from your iPhone.

As a commenter mentioned, keeping the app open on the iPhone will minimize your annoyance.