Wine (Windows) System Tray does not work in Ubuntu. There are two options:
1. Emulate a virtual desktop
Use POL -> Configure -> [select app] -> Wine -> Configure Wine -> Graphics -> Emulate a virtual desktop
to run the application from the virtual desktop. When you run the application this way, it runs in a small windows screen with a System Tray. Once the application is minimised to the System Tray, you can left-click it. I couldn't get right-click to work.
2. Indicator Systemtray Unity App
The Indicator Systemtray Unity app by GGleb adds the Wine (Windows) System Tray into the Unity Application Indicator.
sudo apt-add-repository ppa:fixnix/indicator-systemtray-unity
sudo apt-get update
sudo apt-get install indicator-systemtray-unity
You may need to reboot to get the System Tray to show up. As before, left-click worked for me but right-click did not.
winetricks -q --unattended dotnet45