The handy invisible mode option in Gmail chat does not seem to be working the way it should be. A number of users have found that they are visible in Gmail chat to their contact list even if they had chosen to remain invisible for obvious reasons. It may look you are invisible to you, but to others you are visible and available.
Most users won’t even know they are facing this problem until someone pings. As of now, it seems only a few users are affected by this problem. However, it is not clear how prevalent this issue is. Although users have raised this issue at the Google/Gmail support forum Google has not said anything in the forum.
Annoying aspect of the problem is that it does seem to be reproducible, even for the affected users. Some users face this issue only when they login for the first time. They become invisible later in the day. Also, a few users are visible (and available) for a long time after they have logged out from Gmail. A bug in Gmail chat or a browser/cache issue?
Temporary Solution to Gmail Invisible Bug
One of the users suggested this solution in Google support forum; Every time after logging in “change to visible mode” for a couple of seconds and “change back to invisible mode”. It seems to solve the problem.