So this problem is solved by exporting the avatar mesh and animations using 3Dxchange and in Unity turning the animation type from humanoid (which is the default choice made by Auto Set-up for Unity) to generic. Only turning the animation type of the avatars and motions exported from iClone and CC3 to generic doesn't make any difference. When I exported, a dialog popped up saying that CC3 and iClone are recommended. Just ignore this warning if you need to implement the same feature as mine. Another thing that's worth noting is that, you'll probably need to export the avatar from CC3 first using Auto Set-up for Unity to obtain the materials. Although 3DXchange provides multiple choices for textures, it doesn't work at all on my end. The avatar is all white after imported in Unity and no materials are generated. Fortunately they use the same name for the materials so you can just copy and paste the material and texture folders from the one exported from CC3 and re-attach the materials manually. 

All in all, there are two main ways that I tested workable for exporting visemes. If you want to create facial animations TOGETHER WITH body motions and JUST PLAY these, exporting the animation clips as iMotionPlus is a good way. However, if you want to modify the joints in Unity after exporting, 3DXchange is the proper one to choose. Hope this helps and hope the reallusion team can make the exporting process cleaner in the future versions.