If you were to flip it upside down then yes it would go on top. It's more of a rear lip. Here's the official directions for the install. *note, change "nu" to "new" in the URL*http://www.nucelica.org/other/installs/trdkit/rearval.pdf
That being said, when I did mine, I didn't remove the rear wheels, I took the bumper off instead. I did this because you have to drill 4 holes in the bumper and it's pretty tight under there. I hummed and hawwed about drilling the holes but decided this: 1;I'm not going to be taking it off any time soon, & 2; If I'm going to do this, I'm going to do it right.
So after taking out the rear trunk plastics and taking the bumper off, there are 4 little "X"'s marked on the inside of the bumper. Drill those out.
I bought some clips from an automotive store, I think they're called speed clips or something. You put them over the plastic and they give you a hole to screw into. I put these clips on the 4 clip parts on the valence. Then I got some 2 sided tape, and put it on the top parts of the bumper. I test fit it a few times to make sure it fit. Then I screwed it down (the 4 holes I drilled out) Also like it says in the directions, pull up about an inch of 2 sided tape & have it poking above the rim of the top piece.
One thing I may have done wrong is this. I might have done up the screws a bit too tight. The valence has the cut outs for the black piece on the bumper. It's supposed to sit on this "shelf" but mine sits a bit higher. Now that I look at the pic in the corner of the black you can see the valence sitting nice and tight, so I guess that's just the way it fits.
Ok so screw the 4 screws on the inside of the bumper down. Kinda play with it until you find where it lays down on the bumper nice. It's Urethane so it has some give and flex. It should lay down ok. Then line up the holes & drill those in. Place some more clips on the original bumper (underneath so the screws will go into them) Then screw it down. After that pull on the little pieces of 2 sided tape (the red cover) and it should pull out from between the valence and the bumper and press them together.
Voilla. Put the bumper back on, put the plastics back in and you're good to go.
But seriously, go by the PDF thing. Those are the "real" directions.
Oh, and you'll have one or 2 extra screw holes on the bottom inside the wheel well. On the actual TRD
editions, there is a little piece of plastic that bolts onto that and fills in the area between the 2 bumpers. So nothing goes there. Don't sweat it.
Here's a pic of mine installed. Oh there's an assload of screws on the bumper to take it out. Keep searching for them. Jesus Mruphy I just wrote a book.