Safari browsing visible on other devices

I'm having a few problems with privacy issues. I share an icloud account with my kids and have realised that whenever I open safari on my macbook, the kids can see it on their ipads/iphones. I have tried adjusting the settings on my mac so that this doesn't happen but it doesn't seem to make any difference. The only way I seem to be able to stop it is if I use a private browsing window (by clicking 'file', 'new private window'), but it's a bit of a pain having to do this every time I open safari. Surely theres a way to just turn it off? I've managed to stop it the other way (iphone browsing history showed up on my macbook before but thats stopped now). I don't want to turn icloud off as find some of the features useful such as for syncing calendar entries etc with my phone, but neither can I have the kids watching everything I look up on the internet (and in case you're thinking it no i'm not talking about dodgy adult sites).