There is a work-around.
Before pasting the mask, select the target layer and Pre-Compose it (Layer > Pre-Compose). You’ll see a dialog that gives you two options – in this case you, want the second one.
Pre-Composing means: Take the layer(s) I selected, cut them from the Comp I am in, create a new Comp that is nested inside this one, and paste the selected layer(s) inside that one.
So if you paste in the Pre-Comp (ie, from the main Composition) the mask will fit perfectly.
But what if you want to scale the image inside the mask? The original layer still has is its’ own scale property. If you double click the Pre-Comp, you’ll go inside the Pre-Comp and you’ll be able to edit the orginal layer’s scale.
Why are we doing this?
Because After Effects has a specific order for processing. Transform (for example, scale) always is done after masks, so when you scale down a layer, you’re scaling down them masks.
When you Pre-Compose a layer, you make sure that everything inside is calculated before. So, the layer inside the Pre-Comp is scaled, then the whole Pre-Comp is masked.
But, you say, if I do that, I can’t see its’ relationship to the mask as I scale it down!
Here’s when you can get all fancy and impress your friends.
If both the parent Comp and the Pre-Comp are available as tabs in the timeline (ie, they are both “open”) you’ll see you can enable a lock for the parent Comp in the upper left corner of the Comp panel. If you enable that lock, you can switch in the timeline to the Pre-Comp tab, adjust scale as you see the results in the parent Comp (don’t try to adjust it directly in the Comp panel, just drag the scale property in the timeline).
Too complicated?
Adolfo Rozenfeld · Adobe