According to Skype team, if you are signed in to Skype on multiple devices (a laptop, tablet and a smartphone) and you are sending chat messages to a group of friends from your tablet. Skype will only send new message notifications to your tablet and not to any of your other devices.
If you stop actively using Skype on all devices, the notifications will again start coming on all connected devices, so that you don’t miss them. Skype doesn’t mention what is “actively using” for it but it will most likely take into account the time Skype is not used on a particular device.
The new feature will be rolled-out to all Skype users in the next few weeks. Make sure all your Skype apps are on the latest version.
