On/of

On/of
 

is it correct to use ON?

-Our argument against this hypothesis and evaluations __ that.

In dictionaries I can only find OF; do you think ON is less common or simply wrong?

You can have an hypothesis on something. "The hypothesis on the evolution of PMS" came up in a google search.

You can be evaluated on your teamwork. You can't be evaluated of your teamwork. Yet you can get an evaluation of your teamwork. An evaluation on your teamwork seems wrong to me.

I don't know, but the general rule here seems to be:
verb: evaluate [someone] on [something].
noun: an evaluation of [something].

Excellent answer. Thank you.