Just to confirm, you made the left and right profiles inside of Character Animator by duplicating and repositioning layers, and you want that to reflect back in the PSD?
If so, unfortunately, you'll need to do the work again because the link is one way from Photoshop > Character Animator, not the other way around. It's much slower to make puppet edits inside of CH and you should always be updating art inside of PS or AI. The duplicates you made in CH (again, if that's what you ended up doing) are just references of the art from PS. You can see this in action by doing something like changing the color of a layer in PS and watching it update on all of your profiles back in CH.