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If the elevator is behind the center of mass/lift they need to push the back down, so they need to point up to raise the nose of the aircraft (other side of cg/cl).

If the surfaces are in the front of cg/cl, they need to do the opposite. To pull the nose up, they would have to point downwards.

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Exactly. The site calls them ailerons (presumably because they are on the wing and can roll the plane) but they are quite far back from the cg and so function more like elevators when used together.

Concorde worked this way [1], and called them 'elevons'. When I used to work on Tornados these were called 'tailerons'.

[1] https://www.heritageconcorde.com/roll-pitch-and-yaw

Edit: The original site actually describes them correctly here, so I assume the text on the front-page is just a typo: https://www.foldnfly.com/lounge/steer-aim.php#elevon

More accurately, they are "elevons."

(And yes that's a word)

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