I can only suggest what I suggested in your other thread ...
Open mail in your browser, then click on Options, then on Privacy, then on Advanced. Scroll down the page a bit and move the slider bar beside Private Messages to No one, scroll down a bit further and click on save.
I have no idea if that will do it or not, but you can only try. I use exactly the same version and build of messenger that you have and, as far as I know, none of my contacts can see that I'm on line when I am using mail, nor do I get any IM messages popping up in mail