Incorrect. Hans was heavily involved with the first. And, yes, Klaus was involved as well, since his name is on the front of the soundtrack.
I think it was a partnership of sorts, like John Carpenter and Alan Howarth collaborating on Halloween 2.
If you listen to COTBP, DMC and AWE soundtracks, I find I think Klaus Badet had more influence on Curse's score, Zimmer's got a distinct style and all of his films feel like a piece of a collection, like Williams and Goldsmith, and Curse just sounds different from the other 2 films.