The FaceCenterAttachment value in the mentioned bundle (https://www.roblox.com/bundles/1312/) is significantly off (0, -0.094, 0.001), so it’s expected that the accessory mentioned in the original post (https://www.roblox.com/catalog/14930656829/Mask), which uses FaceCenterAttachment, naturally shifts downward.
The attachment values currently set by Roblox are:
FaceCenterAttachment: 0, -0.094, 0.001
FaceFrontAttachment: 0, -0.037, -0.594
HairAttachment: 0, 0.607, 0.001
HatAttachment: 0, 0.607, 0.001
NeckRigAttachment: 0, -0.586, 0.001
For Roblox, the attachment positions I would recommend are:
FaceCenterAttachment: 0, 0, 0
FaceFrontAttachment: 0, 0, -0.6
HairAttachment: 0, 0.6, 0
HatAttachment: 0, 0.6, 0
NeckRigAttachment: 0, -0.5, 0
Since FaceCenterAttachment should be located at the exact center of the head, it should be set to 0, 0, 0 (or very close to it) instead of 0, -0.094, 0.001; the -0.094 offset is especially problematic.
I fixed this for Roblox in the video (please hire me if setting up these heads is this hard 

)