I believe it is supposed to go under the clips, but mine usually just winds up waving in the breeze or in the trash. The brakes generate dust that has to escape anyway, so trying to seal against dust never made any sense to me.
If the shoe tops are different, I suspect you've got one of them turned backwards or have the wrong shoes. The ends that go against the adjuster should be the same. The other end of the trailing shoe (the one without the lever) may or may not have the hole for the handbrake lever, though.
There's an illustration on page 409 of the TR6 Bentley.