I have an iPad, an iPhone, and a Mac. They are on 11.4. and on 10.13.5.
iMessage is active on all 3 devices. iCloud is active for iMessage on all 3 devices.
I logged out from iCloud on all 3 devices, and logged in again.All 3 devices were on charger, just to be sure.
All 3 devices are in a 2 meters distance from my Wifi router, signal ist very strong, and all devices are connected to the internet via Wifi.
I sent an iMessage from my Mac, and received a response, which instantly synched between the Mac and the iOS devices.
Then I deleted the message from my Mac. This was about 90 minutes ago, and the message is still on both iOS devices.
All other Wifi related activities on my Mac, my iOS devices, my TV, my home control system etc., work flawlessly, and with high speed (Netflix, Amazon, Onedrive big files transfer, iTunes downloads, turning lights on/off etc.).
It's just this new iMessage feature that doesn't work properly.