GTALK- Logged In constantly when choses as authentication method?

So I was trying to figure out why/how people were constantly asking me why I was not responding to them on Gtalk (IM) . Turns out when I thought I was logged off my 2 other machines running Jump Desktop were actually keeping me logged in. I chose to use Google to authenticate my remote desktops- so I guess it shows me logged into google 24/7???

Has anyone else noticed this?