Deleting photos on Google+ doesn't delete them on local storage on my phone

I'm still getting used to the Auto Backup functionality in the Photos app. I turned this feature on and all my photo's are correctly synced to Google+. When I delete a photo on my phone (Nexus 5) it also gets deleted on Google+. However, when I delete photos on the Google+ website, they don't get deleted on my phone. Is this just how this thing works, or is there something wrong in my setup? I tried turning off Google+ photo sync in the settings, but that didn't change anything. When I delete it on the Google+ web page, it says the photos will also be deleted on all synchronized devices, so isn't that how it's supposed to work then? It would make it a whole lot easier to delete photos that I don't need on a big screen like my laptop, and to have them automatically deleted on my phone to free up storage space.