To my knowledge (which is still somewhat limited on it) - it has something to do with exported joints in the mesh item you equip. I don't know exactly what causes it (and have not been able to get clarification from anyone as to how to avoid it) - but I think the mesh-maker has to be sure that they don't change/deform the rig while they weight the mesh (I think that can mesh with the joints somehow?) And also, not to include the joint export thing unless it's necessary. (Again I could be talking gibberish here, because I really haven't gotten clarification on -why- or -how- this happens, only that this can cause rigged mesh to bug the eyes of avatars.)
The suggestion of using smaller eyes etc. is great except... it means changing eyes with every outfit based on if the outfit causes it to bug or not. I've run into a few other items for Kemono that have this issue, including a skirt and a sweater, and they've all had the same issue with no resolution -__- If anyone has more insight into why this is occurring, it would help the greater Kemono community IMO, especially those learning/newer to meshing, to keep this from happening.
As for the OP, I guess contact the creator and see if they have updated the product yet to fix the issue. If not, you're stuck using other eyes that can be tweaked. (For mine I had to move them back, and set them down lower by just a tad, to get them to work normally again.)