Sorry, I'm going to ask some obvious questions here.
Do you have the correct cyrillic fonts installed?
Does cyrillic work in other programs (i.e. when not running wine)?
If yes, how did you configure your computer to switch between the two keymaps?
(For example, I changed my settings in /etc/X11/XF86Config-4(5), but I think there are several different ways to do it.)
Have you read this thread?