I'm assuming the issue is with the eye shape customization not working well with MMD. I'm able to correct it for most things by turning off the shapes when the eyes are closed for things like expressions and face tracking, but unfortunately there doesn't seem to be a way for me to do that with MMD. For now, my only easy suggestion is to turn down or disable any eye shape/size customization when using MMD.
The only other possible option I can think of at the moment would be to go through and edit the avatar mesh's MMD shapes to account for whatever customization shapes you're using, but that would require editing the avatar's FBX.