What am I missing?
Pretty much everything about masks (no offense).... Unless referenced in an effect, masks do not constrain anything. It's inherent how AE's render pipeline works. Therefore, you would need to work with a duplicate of the layer and put the blurred version on top of the unblurred one. and don't forget to set the mask mode then, which also does not seem to be the case with your current setup or else you should have seen the unwanted parts disappear....
This video shows the application of an effect to a small part of a scene by applying the effect to an adjustment layer with a mask on it:
That should give you the basic idea.
Since you're new to After Effects, I recommend that you start here.
Thanks, but I already tried the obvious, such as you suggest — putting a blurred version behind an unaltered frame — works, but primitve. I was looking for something with finer control.
Perfect, exactly what I was looking for.