From the start, you want to treat your interviewer as your advocate to the college you are applying.
Use every opportunity to remove her doubt about you. There is no harm in telling the interviewer what other colleges you are applying, unless you are applying ED.
If you are a strong applicant and you are applying to a competitor college, you want your interviewer to know that. You want your interviewer to advocate on your behalf to convene your outstanding qualifications to the college. Withholding that information when prompted will only cast doubt in the interviewer's mind, and he or she may draw a wrong conclusion or impression, or otherwise unfavorable opinion of you.
Treat it as a non-issue.