Westaff is a temp agency that I've seen in more than one state that I've lived in, so it's certainly not something just local to you.
I've never been to one. My wife has gotten two different jobs through temp agencies, both of which led to full-time positions. In both instances she reported her hours worked to the agency, they produced her paycheck, and they produced her W-2 at the end of the year.
The temp agency is paid a fee by the employer, just like an airline may pay a fee to a travel agent.
The impression I get is that many companies have reduced or eliminated their own Human Resources Department and now let the temp agencies do some of the work the company used to. The use of temp agencies also allows the companies to avoid paying benefits for just a little bit longer than they used to, and it reduces possible liability in that prospective employees are kept in an "at-will" status longer than typical for that employer.
My wife is college educated and was actually looking for full-time work and both times using an agency her temp work quickly led to full-time. For someone who wants just a couple of months work, I would think that tele-marketing or day labor may be more likely what they have for you. I could easily be wrong.
It doesn't cost you anything to check it out and I can't imagine what the negatives would be. I'd certainly be interested to hear what you find out if you contact them.