I don't think it is you mate ... I have never been able to get TS Notifier to work either and it appears we are not alone!
In my case it would work when in the game menu screens but not when I actually entered the cockpit... Weird.
I use the overlay that comes with TS3 itself... And I couldn't get that to work initially either
there is a handy thread in the team speak section on ATAG which has some pretty clear instructions and after following those I was able to get the default overlay to work in game... You might want to give that a crack.
Having said that, if you have TS showing on another screen then it's probably moot anyway.
I tried the sound reduction thingy in TS but didn't like it as the constant increase/decrease of game sounds just got annoying for my tastes. All I do instead is minimize the game prior to jumping in the cockpit and click on the little volume icon at the bottom of the screen and set the overall sound slider up higher but reduce the slider for Cliffs ... I eventually found a balance between the two where I can clearly hear people speaking and still get decent game volume as well. Works well enough.