Games : How to deny people to see when I was online on steam?

I always start my steam, with the following setting set on disabled: "Automatically sign into Friends when I start Steam".

It seems to work, people can't see if I'm online. But when I check profiles of my steam buddies, there I can find myself and the time when I was "Online last time".

There the last time is always set to the time when I logged in into my account. I don't like it, how to disable this?