The last paragraphs cover the vertical adjustment.
Most adjustments like this are a bit finicky. Usually they take just a slight nudge to see a change. Sometime putting a screwdriver into a slot are putting a bit of pressure on it will do the deed. No need to do any twisting or turning, that's gross adjustment.
Anyway slightly loosen the screw holding the beamsplitter. Don't loosen lit enough to be free. You need the friction to hold it in place when you apply just a touch of pressure..
If you can see the bracket move, that's likely too much.