Anyway, I found the solution myself, in case someone else has problems.
The solution is to set refresh rate to 60Hz and turn VSYNC On, because the mouth animations are not properly timed, but tied to number of frames. It probably affects only people with 120Hz monitors.
I hate to grave dig your post, but I can't seem to make a new post on here. My monitor is at 60Hz by default, yet I experience the mouth moving too fast problem. My monitor can do 4K, but it is set to 1080p right now so I don't think that is the problem. Any suggestions?
Sorry for the late reply, check if you have VSYNC on, you will find it in the setting of your GFX card drivers. VSYNC forces to synchronize frame rendering with refresh rate of your monitor - so when you have 60HZ monitor, game will run precisely on 60 HZ (or on 30, if it cannot render the frame in time). If you leave VSYNC off, refresh rate of your monitor and frame rendering of your GFX card will be independent (asynchronous). I hope this explanation is clear enough.