Both חשיפה and exposure are odd concepts in that they are not necessarily affected much by a reversal of directionality.  For example, if a rabbi exposes his sense of humor to his students, he has also exposed his students to his sense of humor and the phrasings differ little in their meaning.  I suppose the difference is in a choice of emphasis:  on the thing that has previously remained in concealment, or on the people who have previously remained unaware.