I'm not sure anything is wrong. You're expanding a feathered mask and your 'how it looks' shows the effect of an expanded mask where it's cutting into the chin of the character. Do the mask points move when you scrub through the timeline? If they do then they are just not in the right position to preserve the chin of your character.
If you've set keyframes and the mask shape doesn't move then purge your cache completely and let us know if that fixes the problem.
I'm trying to animate position of the mask, so I'm moving the whole mask every frame, but when I move it, I can't see any changes, it shows me result like if the mask was in position from the frame before. Purging my cache works, but it only refreshes one frame and then I have to do it again for the next one.
First, try turning off disk cache. Maybe that's what is fouling up your previews. Second, make sure you are efficiently animating your mask. I can't recall ever having to move a mask on every frame. My technique is to set a keyframe at the start of the mask animation, them move to the last frame and reposition the mask, then check half way through the move to see if there are any adjustments that need to be made, then split the difference again. The fewer keyframes you have in the time line the better the animation will look.
if you have a lot of camera movement in the mask then stabilize the shot first and animate the mask, then remove the stabilization and add the tracking info to the mask. Check out this quick example I did and observe the technique. I prefer to add a colored solid that I will use as a track matte instead of directly masking on the footage.
There's a better way to remove the stabilization and add it to the mask layer with a null and parenting in this video so you don't have to reposition the mask layer.
Instead of adding a target as a track matte you would just draw the mask on the solid... Sorry, there's no audio in the second video.
Alright, I've tried turning off disk cache, but that didn't help. I'm animating avery frame, because the way my stopmotion is made is that there are some frames repeated 2 times, some 3 times, some are there only once, and with such diversity, it seems doing it frame by frame is the best option. Still, thank you for interesting tutorials.