Stop sharing activities between different devices

I couldn't find the answer to this, because it is a very hard to explain annoying issue. Since a while now, whenever I open Safari or another app on my iPhone I get to see this on my MacBook. Let me explain: The app that I use on my iPhone, for example Safari, pops up on my MacBook screen and when I click it on my MacBook I see the webpage that I am visiting on my iPhone appear on my MacBook and I don't want this. In the system preferences of both devices 'Safari' is 'OFF' in the icloud settings. Still it doesn't matter what I do, I always get to see on every device what the others device 'is doing'. The only thing that seems to help is logging off of my icloud account on one of my devices, but then I don't get to use other icloud features.

Does somebody have a solution for this? How to stop the devices from 'seeing each other's activities in realtime', but nog having to log off my icloud account.