Masks, layers, solids or multi composition to solve my problem?
The answer to your question is yes. Masks, solids or multi-compositions will help.

What, you want more? Oh ok. 

Thing about After Effects is that there is almost always at least two valid ways of doing anything: 

To fix your problem you could use masks on each eye. Now because you're scaling the layers, and masks are attached to a layer and scale with it, that won't really work (You could scale down the mask to match the scale of the layer, but getting that right might be really tricky, so I wouldn't recommend it). So if you want to use a mask on the layer you have to pre-compose the layers, with the attributes included, so the scale keyframes are inside the new pre-comp, and then apply the mask in the original comp. 


Pros: simpler timeline, 
cons: the keyframes are now in two other comps, so you have to be switching between them, and copying-pasting to make any edits (you could synchronise them with expressions though).


Another method would be to make track mattes for each eye. You do this by using any layer–usually a solid–and putting it above the layer you want to mask, and then turning on alpha matte on the layer you want to mask - each eye in this case. 



This works a bit like stencil/silhouette alpha mode, except that it only affects one layer. You can either resize the matte layer or use a mask to make the matte the right size. 


Pros: everything is on the one timeline, easy to edit. 
cons: more layers on your timeline, you have to remember to keep the track matte and footage layer together if you're changing the position of your layers.