I also got a call from this number, with the same message as above, only from a guy named Fred. I believe this is a scam. I did not call them back either.

Someone named Tiffany called me today saying that my number was passed across her desk, and that it came to her attention that I was looking for some part time job.

Interestingly, she did not know my name.

She didn't know who I was, but somehow she knew I was looking for work.

Sounds like a phishing scam.  Don't give her any personal information about yourself.  

She did not identify the name of the company she was working for.